{"id":569,"date":"2026-07-15T03:17:24","date_gmt":"2026-07-15T03:17:24","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=569"},"modified":"2026-07-15T03:17:25","modified_gmt":"2026-07-15T03:17:25","slug":"electrical-resistance","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/electrical-resistance\/","title":{"rendered":"What Is Electrical Resistance?"},"content":{"rendered":"\n<div class=\"pf-citation\"><div class=\"eyebrow\">Definition<\/div><p>\nElectrical resistance is a measure of how strongly a component opposes the flow of electric current, defined as the voltage across it divided by the current through it (R = V\/I) and measured in ohms. For a uniform conductor, resistance equals resistivity multiplied by length and divided by cross-sectional area.\n<\/p><\/div>\n\n<p>Reach behind your desk and feel a phone charger after an hour&#8217;s work. It is warm \u2014 not because anything is broken, but because something inside it is fighting the current, and losing that fight as heat.<\/p>\n\n<p>That fight has a name, a symbol and a unit. It also explains why a toaster glows orange while the cable feeding it stays cool, why power stations sit at the end of colossal pylons, and why the wire in your walls is fat, short and made of copper.<\/p>\n\n<h2>What Is Electrical Resistance?<\/h2>\n\n<p>Electrical resistance is the opposition a material or component offers to the flow of electric charge through it. Push charge through anything except a superconductor and something pushes back.<\/p>\n\n<p>Picture water in a pipe again \u2014 the analogy is old because it works. Pressure drives the flow, the pipe&#8217;s narrowness fights it, and what you actually get is the compromise. Resistance is the narrowness.<\/p>\n\n<p>But here is the part worth pausing on. Resistance is not a substance sitting inside the wire; it is a <em>ratio<\/em>, a bookkeeping of how much push you need for how much flow. Give a component one volt, measure one amp, and you have defined its resistance as exactly one ohm.<\/p>\n\n<p>The unit is the ohm, symbol \u03a9, named for Georg Simon Ohm. One ohm is one volt per ampere \u2014 and since the 2019 revision of the SI, the ohm is realised in national laboratories from the quantum Hall effect rather than from any physical lump of metal. NIST&#8217;s <a href=\"https:\/\/www.nist.gov\/programs-projects\/metrology-ohm\" target=\"_blank\" rel=\"noopener\">Metrology of the Ohm<\/a> programme is where that standard actually lives.<\/p>\n\n<h2>The Electrical Resistance Formula: R = V\/I<\/h2>\n\n<p>The defining formula for electrical resistance is the voltage across a component divided by the current through it.<\/p>\n\n<div class=\"pf-formula\">R = V \/ I<\/div>\n\n<ul>\n<li><strong>R<\/strong> \u2014 resistance, measured in ohms (\u03a9)<\/li>\n<li><strong>V<\/strong> \u2014 potential difference across the component, measured in volts (V)<\/li>\n<li><strong>I<\/strong> \u2014 <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/electric-current\/\">electric current<\/a> through the component, measured in amperes (A)<\/li>\n<\/ul>\n\n<p>The units close the loop neatly: 1 \u03a9 = 1 V\/A. A component that draws 0.5 A from a 12 V supply has a resistance of 24 \u03a9, and you can check that in seconds with our <a href=\"https:\/\/physicsfundamentalsinfo.com\/calculators\/ohms-law\">Ohm&#8217;s Law Calculator<\/a> if you would rather not reach for a pen.<\/p>\n\n<p>This equation is the rearranged form of <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/ohms-law\/\">Ohm&#8217;s law<\/a>, and that relationship deserves its own careful treatment. Here, though, R is the star rather than the supporting act \u2014 so the interesting question is not <em>how do I find R<\/em>, but <em>what decides what R is in the first place?<\/em><\/p>\n\n<p>Because R = V\/I is a definition, it works on anything: a resistor, a diode, a cucumber. What it does <strong>not<\/strong> promise is that the number stays put. For a metal at steady temperature it does. For a filament lamp it climbs as the lamp heats.<\/p>\n\n<p>Engineers name that distinction. The plain V\/I ratio at one operating point is the <em>static<\/em> resistance; the slope of the current-voltage curve at that same point is the <em>differential<\/em> resistance. Wikipedia&#8217;s overview of <a href=\"https:\/\/en.wikipedia.org\/wiki\/Electrical_resistance_and_conductance\" target=\"_blank\" rel=\"noopener\">electrical resistance and conductance<\/a> sets the two side by side, together with conductance, the reciprocal quantity you will meet shortly.<\/p>\n\n<h2>What Sets Electrical Resistance? The 4 Key Factors<\/h2>\n\n<p>Four things decide a conductor&#8217;s resistance: what it is made of, how long it is, how thick it is, and how hot it is. The first three are bundled into one compact formula.<\/p>\n\n<div class=\"pf-formula\">R = \u03c1L \/ A<\/div>\n\n<ul>\n<li><strong>R<\/strong> \u2014 resistance, in ohms (\u03a9)<\/li>\n<li><strong>\u03c1<\/strong> (rho) \u2014 resistivity of the material, in ohm-metres (\u03a9\u00b7m)<\/li>\n<li><strong>L<\/strong> \u2014 length of the conductor, in metres (m)<\/li>\n<li><strong>A<\/strong> \u2014 cross-sectional area, in square metres (m\u00b2)<\/li>\n<\/ul>\n\n<p>Read the formula as a sentence and it stops being algebra: longer means harder, fatter means easier, and the material sets the exchange rate. If you would rather see where it comes from than take it on trust, the OpenStax chapter on <a href=\"https:\/\/phys.libretexts.org\/Bookshelves\/University_Physics\/University_Physics_(OpenStax)\/University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)\/09:_Current_and_Resistance\/9.04:_Resistivity_and_Resistance\" target=\"_blank\" rel=\"noopener\">resistivity and resistance<\/a> at Physics LibreTexts derives it from current density.<\/p>\n\n<svg role=\"img\" aria-label=\"Diagram showing electrical resistance R = rho L over A, with a long thin wire having four times the resistance of a short fat wire of the same material\" viewBox=\"0 0 700 400\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:100%;height:auto;max-width:700px;display:block;margin:24px auto;\">\n  <rect x=\"0\" y=\"0\" width=\"700\" height=\"400\" fill=\"#F5F2EA\"><\/rect>\n  <text x=\"350\" y=\"30\" font-family=\"Georgia, serif\" font-size=\"17\" fill=\"#0A1628\" text-anchor=\"middle\" font-weight=\"bold\">The anatomy of R = \u03c1L \/ A<\/text>\n\n  <!-- main wire -->\n  <rect x=\"150\" y=\"62\" width=\"400\" height=\"46\" fill=\"#C8932A\" opacity=\"0.30\" stroke=\"#C8932A\" stroke-width=\"1.5\"><\/rect>\n  <ellipse cx=\"150\" cy=\"85\" rx=\"9\" ry=\"23\" fill=\"#7A1F2B\" opacity=\"0.55\" stroke=\"#7A1F2B\" stroke-width=\"1.5\"><\/ellipse>\n  <ellipse cx=\"550\" cy=\"85\" rx=\"9\" ry=\"23\" fill=\"#C8932A\" opacity=\"0.45\" stroke=\"#C8932A\" stroke-width=\"1.5\"><\/ellipse>\n  <text x=\"112\" y=\"90\" font-family=\"Georgia, serif\" font-size=\"13\" fill=\"#7A1F2B\" text-anchor=\"middle\" font-weight=\"bold\">A<\/text>\n  <text x=\"350\" y=\"90\" font-family=\"Georgia, serif\" font-size=\"13\" fill=\"#0A1628\" text-anchor=\"middle\">resistivity \u03c1 (the material)<\/text>\n  <line x1=\"150\" y1=\"128\" x2=\"550\" y2=\"128\" stroke=\"#0A1628\" stroke-width=\"1.5\"><\/line>\n  <line x1=\"150\" y1=\"122\" x2=\"150\" y2=\"134\" stroke=\"#0A1628\" stroke-width=\"1.5\"><\/line>\n  <line x1=\"550\" y1=\"122\" x2=\"550\" y2=\"134\" stroke=\"#0A1628\" stroke-width=\"1.5\"><\/line>\n  <text x=\"350\" y=\"146\" font-family=\"Georgia, serif\" font-size=\"13\" fill=\"#0A1628\" text-anchor=\"middle\">length L<\/text>\n  <text x=\"112\" y=\"106\" font-family=\"Georgia, serif\" font-size=\"10\" fill=\"#7A1F2B\" text-anchor=\"middle\">area<\/text>\n\n  <line x1=\"60\" y1=\"172\" x2=\"640\" y2=\"172\" stroke=\"#D9CFB8\" stroke-width=\"1.5\"><\/line>\n  <text x=\"350\" y=\"196\" font-family=\"Georgia, serif\" font-size=\"13\" fill=\"#0A1628\" text-anchor=\"middle\" font-style=\"italic\">Same metal, same volume of copper \u2014 only the shape changes.<\/text>\n\n  <!-- long thin -->\n  <rect x=\"70\" y=\"228\" width=\"330\" height=\"14\" fill=\"#7A1F2B\" opacity=\"0.35\" stroke=\"#7A1F2B\" stroke-width=\"1.5\"><\/rect>\n  <text x=\"235\" y=\"222\" font-family=\"Georgia, serif\" font-size=\"12\" fill=\"#0A1628\" text-anchor=\"middle\">long and thin<\/text>\n  <text x=\"235\" y=\"262\" font-family=\"Georgia, serif\" font-size=\"13\" fill=\"#7A1F2B\" text-anchor=\"middle\" font-weight=\"bold\">R = 4R<tspan dy=\"3\" font-size=\"9\">0<\/tspan><\/text>\n  <text x=\"235\" y=\"280\" font-family=\"Georgia, serif\" font-size=\"11\" fill=\"#0A1628\" text-anchor=\"middle\">2L, half the area<\/text>\n\n  <!-- short fat -->\n  <rect x=\"470\" y=\"221\" width=\"165\" height=\"28\" fill=\"#C8932A\" opacity=\"0.40\" stroke=\"#C8932A\" stroke-width=\"1.5\"><\/rect>\n  <text x=\"552\" y=\"212\" font-family=\"Georgia, serif\" font-size=\"12\" fill=\"#0A1628\" text-anchor=\"middle\">short and fat<\/text>\n  <text x=\"552\" y=\"272\" font-family=\"Georgia, serif\" font-size=\"13\" fill=\"#0A1628\" text-anchor=\"middle\" font-weight=\"bold\">R = R<tspan dy=\"3\" font-size=\"9\">0<\/tspan><\/text>\n\n  <text x=\"435\" y=\"243\" font-family=\"Georgia, serif\" font-size=\"20\" fill=\"#0A1628\" text-anchor=\"middle\">vs<\/text>\n\n  <rect x=\"70\" y=\"306\" width=\"565\" height=\"66\" fill=\"#0A1628\" rx=\"3\"><\/rect>\n  <text x=\"352\" y=\"330\" font-family=\"Georgia, serif\" font-size=\"13\" fill=\"#FAF6EE\" text-anchor=\"middle\">Double the length and halve the area and you multiply resistance by 4.<\/text>\n  <text x=\"352\" y=\"354\" font-family=\"Georgia, serif\" font-size=\"13\" fill=\"#C8932A\" text-anchor=\"middle\">Not one atom of copper was added or removed.<\/text>\n<\/svg>\n\n<p style=\"text-align:center;font-size:13px;font-style:italic;\">Resistance is set by the material (\u03c1) and the shape (L and A) together \u2014 stretch the same metal and R climbs.<\/p>\n\n<h3>1. The material \u2014 resistivity (\u03c1)<\/h3>\n\n<p>Resistivity is the material&#8217;s own contribution, independent of shape. It is why copper wires your house and glass insulates a pylon.<\/p>\n\n<p>The span is genuinely staggering: from silver at 1.59 \u00d7 10<sup>\u22128<\/sup> \u03a9\u00b7m to glass at around 10<sup>14<\/sup> \u03a9\u00b7m is roughly twenty-two orders of magnitude \u2014 one of the widest ranges of any physical property. Nichrome, the alloy in your toaster, is about 65 times more resistive than copper. That single ratio is why one glows and the other does not.<\/p>\n\n<h3>2. Length (L)<\/h3>\n\n<p>Resistance is directly proportional to length. Double the wire, double the resistance \u2014 every extra metre is more lattice for the electrons to bump through.<\/p>\n\n<h3>3. Cross-sectional area (A)<\/h3>\n\n<p>Resistance is inversely proportional to area, and this is where intuition quietly fails. Area depends on the <em>square<\/em> of the diameter, so doubling a wire&#8217;s diameter does not halve its resistance \u2014 it quarters it.<\/p>\n\n<h3>4. Temperature (T)<\/h3>\n\n<p>Heat a metal and its resistance rises. The ions vibrate harder, electrons collide more often, and the material fights back more. For modest temperature changes the relationship is close to linear:<\/p>\n\n<div class=\"pf-formula\">R = R<sub>0<\/sub> \u00d7 (1 + \u03b1 \u00d7 \u0394T)<\/div>\n\n<ul>\n<li><strong>R<\/strong> \u2014 resistance at the new temperature, in ohms (\u03a9)<\/li>\n<li><strong>R<sub>0<\/sub><\/strong> \u2014 resistance at the reference temperature (usually 20 \u00b0C), in ohms (\u03a9)<\/li>\n<li><strong>\u03b1<\/strong> (alpha) \u2014 temperature coefficient of resistance, in per degree Celsius (\u00b0C<sup>\u22121<\/sup>)<\/li>\n<li><strong>\u0394T<\/strong> \u2014 temperature change from the reference, in degrees Celsius (\u00b0C) or kelvin (K)<\/li>\n<\/ul>\n\n<p>For copper, \u03b1 \u2248 3.9 \u00d7 10<sup>\u22123<\/sup> \u00b0C<sup>\u22121<\/sup> \u2014 about 0.39% per degree. It sounds trivial until a motor winding climbs 50 \u00b0C and quietly gains a fifth of its resistance.<\/p>\n\n<p>Semiconductors do the opposite: warm them and resistance <em>falls<\/em>, because heat frees more charge carriers. That inversion is the whole basis of the thermistor in your kettle and your car&#8217;s coolant sensor \u2014 and it is why <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/thermodynamics\/heat-vs-temperature\/\">the difference between heat and temperature<\/a> is worth getting straight before you trust any resistance figure.<\/p>\n\n<p>A practical warning worth carrying: the linear formula is reliable for changes of roughly 100 \u00b0C or less. Push it to a lamp filament at 2,500 \u00b0C and it will mislead you.<\/p>\n\n<div class=\"pf-sim-slot\"><div class=\"pf-sim-slot-header\"><span class=\"icon-dot\"><\/span><span class=\"label\">Electrical Resistance Lab<\/span><\/div><div class=\"pf-sim-slot-body\"><style>.pf-sim-frame{width:100%;border:none;height:600px}@media(max-width:760px){.pf-sim-frame{height:1000px}}<\/style><iframe src=\"\/labs\/resistance.html?embed=1\" class=\"pf-sim-frame\" loading=\"lazy\"><\/iframe><\/div><\/div>\n\n<h2>Resistance vs Resistivity: The Difference That Trips Students Up<\/h2>\n\n<p>Resistance belongs to an object; resistivity belongs to a material. That one sentence resolves most of the confusion in this topic.<\/p>\n\n<p>Ask &#8220;what is the resistance of copper?&#8221; and the question has no answer \u2014 you have to say <em>which piece<\/em> of copper. Ask &#8220;what is the resistivity of copper?&#8221; and there is a single number, 1.68 \u00d7 10<sup>\u22128<\/sup> \u03a9\u00b7m, true for every scrap of it at 20 \u00b0C.<\/p>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Property<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Resistance (R)<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Resistivity (\u03c1)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Belongs to<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">A specific object or component<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">A material, whatever its shape<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>SI unit<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">ohm (\u03a9)<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">ohm-metre (\u03a9\u00b7m)<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Changes with shape?<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Yes \u2014 depends on L and A<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">No \u2014 intrinsic to the material<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Changes with temperature?<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Yes<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Yes<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Reciprocal quantity<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Conductance G = 1\/R, in siemens (S)<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Conductivity \u03c3 = 1\/\u03c1, in S\/m<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Typical question<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">&#8220;What is this wire&#8217;s resistance?&#8221;<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">&#8220;Is this metal a good conductor?&#8221;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>The link between them is the formula you already have. Resistivity plus geometry gives resistance \u2014 and rearranging lets you go the other way, measuring \u03c1 from a sample: \u03c1 = RA\/L. Georgia State&#8217;s <a href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/electric\/resis.html\" target=\"_blank\" rel=\"noopener\">HyperPhysics summary of resistance and resistivity<\/a> is a compact reference if you want the bulk-property view alongside this one.<\/p>\n\n<p>Here are representative values at 20 \u00b0C, with the temperature coefficient that tells you how fast each one drifts.<\/p>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Material<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Resistivity \u03c1 at 20 \u00b0C (\u03a9\u00b7m)<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Coefficient \u03b1 (\u00b0C<sup>\u22121<\/sup>)<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Why it is used<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Silver<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">1.59 \u00d7 10<sup>\u22128<\/sup><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">3.8 \u00d7 10<sup>\u22123<\/sup><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Best metallic conductor; specialist contacts<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Copper<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">1.68 \u00d7 10<sup>\u22128<\/sup><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">3.9 \u00d7 10<sup>\u22123<\/sup><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Household wiring \u2014 nearly as good, far cheaper<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Aluminium<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">2.65 \u00d7 10<sup>\u22128<\/sup><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">3.9 \u00d7 10<sup>\u22123<\/sup><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Overhead power lines \u2014 light enough to span pylons<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Tungsten<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">5.6 \u00d7 10<sup>\u22128<\/sup><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">4.5 \u00d7 10<sup>\u22123<\/sup><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Lamp filaments \u2014 survives white heat<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Nichrome<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">\u2248 1.1 \u00d7 10<sup>\u22126<\/sup><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">0.4 \u00d7 10<sup>\u22123<\/sup><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Heating elements \u2014 resistive and barely drifts when hot<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Glass<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">10<sup>10<\/sup> to 10<sup>14<\/sup><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">\u2014<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Insulators on pylons and circuit boards<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Treat these as good representative figures rather than gospel \u2014 published values shift with purity, alloy composition and the reference you consult.<\/p>\n\n<p>Notice nichrome&#8217;s \u03b1. It is roughly a tenth of copper&#8217;s, and that stability is the point: a heating element whose resistance barely moves between cold and red-hot draws a predictable current all day long.<\/p>\n\n<h2>Why Does Electrical Resistance Exist?<\/h2>\n\n<p>Resistance exists because moving electrons collide with a vibrating lattice of ions and lose energy to it. The wire is not an open pipe; it is an obstacle course.<\/p>\n\n<p>Apply a voltage and an electric field appears along the conductor, pushing every free electron \u2014 the same electrostatic push described by <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/coulombs-law\/\">Coulomb&#8217;s law<\/a>. Each electron accelerates, travels a tiny distance, slams into an ion, and surrenders the speed it just gained.<\/p>\n\n<svg role=\"img\" aria-label=\"Diagram showing why electrical resistance exists: an electron accelerating between collisions with vibrating metal ions, converting electrical energy into heat\" viewBox=\"0 0 700 300\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:100%;height:auto;max-width:700px;display:block;margin:24px auto;\">\n  <rect x=\"0\" y=\"0\" width=\"700\" height=\"300\" fill=\"#F5F2EA\"><\/rect>\n  <text x=\"350\" y=\"28\" font-family=\"Georgia, serif\" font-size=\"16\" fill=\"#0A1628\" text-anchor=\"middle\" font-weight=\"bold\">Why resistance exists: accelerate, collide, repeat<\/text>\n\n  <rect x=\"60\" y=\"52\" width=\"580\" height=\"150\" fill=\"#C8932A\" opacity=\"0.12\" stroke=\"#D9CFB8\" stroke-width=\"1.5\"><\/rect>\n\n  <!-- ion lattice -->\n  <g fill=\"#7A1F2B\" opacity=\"0.75\">\n    <circle cx=\"130\" cy=\"92\" r=\"11\"><\/circle><circle cx=\"250\" cy=\"92\" r=\"11\"><\/circle><circle cx=\"370\" cy=\"92\" r=\"11\"><\/circle><circle cx=\"490\" cy=\"92\" r=\"11\"><\/circle><circle cx=\"600\" cy=\"92\" r=\"11\"><\/circle>\n    <circle cx=\"190\" cy=\"160\" r=\"11\"><\/circle><circle cx=\"310\" cy=\"160\" r=\"11\"><\/circle><circle cx=\"430\" cy=\"160\" r=\"11\"><\/circle><circle cx=\"550\" cy=\"160\" r=\"11\"><\/circle>\n  <\/g>\n  <g stroke=\"#7A1F2B\" stroke-width=\"1.2\" opacity=\"0.45\">\n    <path d=\"M130 74 q6 -8 0 -12 M250 74 q6 -8 0 -12 M370 74 q6 -8 0 -12 M490 74 q6 -8 0 -12 M600 74 q6 -8 0 -12\" fill=\"none\"><\/path>\n  <\/g>\n  <text x=\"130\" y=\"97\" font-family=\"Georgia, serif\" font-size=\"12\" fill=\"#FAF6EE\" text-anchor=\"middle\">+<\/text>\n  <text x=\"250\" y=\"97\" font-family=\"Georgia, serif\" font-size=\"12\" fill=\"#FAF6EE\" text-anchor=\"middle\">+<\/text>\n  <text x=\"370\" y=\"97\" font-family=\"Georgia, serif\" font-size=\"12\" fill=\"#FAF6EE\" text-anchor=\"middle\">+<\/text>\n  <text x=\"490\" y=\"97\" font-family=\"Georgia, serif\" font-size=\"12\" fill=\"#FAF6EE\" text-anchor=\"middle\">+<\/text>\n  <text x=\"600\" y=\"97\" font-family=\"Georgia, serif\" font-size=\"12\" fill=\"#FAF6EE\" text-anchor=\"middle\">+<\/text>\n\n  <!-- electron zig-zag path -->\n  <path d=\"M75 128 L128 108 L150 132 L248 108 L268 134 L368 108 L388 132 L488 108 L508 132 L598 108 L618 130\" fill=\"none\" stroke=\"#0A1628\" stroke-width=\"2.2\"><\/path>\n  <circle cx=\"618\" cy=\"130\" r=\"7\" fill=\"#0A1628\"><\/circle>\n  <text x=\"618\" y=\"134\" font-family=\"Georgia, serif\" font-size=\"10\" fill=\"#FAF6EE\" text-anchor=\"middle\">e<\/text>\n\n  <text x=\"350\" y=\"228\" font-family=\"Georgia, serif\" font-size=\"12\" fill=\"#0A1628\" text-anchor=\"middle\">Each collision dumps the energy the field just gave the electron.<\/text>\n  <text x=\"350\" y=\"250\" font-family=\"Georgia, serif\" font-size=\"12\" fill=\"#7A1F2B\" text-anchor=\"middle\" font-weight=\"bold\">That lost energy leaves as heat \u2014 which is exactly what resistance is.<\/text>\n\n  <text x=\"112\" y=\"192\" font-family=\"Georgia, serif\" font-size=\"11\" fill=\"#0A1628\">vibrating ion<\/text>\n  <text x=\"500\" y=\"192\" font-family=\"Georgia, serif\" font-size=\"11\" fill=\"#0A1628\">drifting electron<\/text>\n  <text x=\"350\" y=\"278\" font-family=\"Georgia, serif\" font-size=\"11\" fill=\"#0A1628\" text-anchor=\"middle\" font-style=\"italic\">A hotter lattice means more collisions, and more resistance.<\/text>\n<\/svg>\n\n<p style=\"text-align:center;font-size:13px;font-style:italic;\">Resistance is billions of tiny collisions per second, converting ordered electrical energy into random thermal motion.<\/p>\n\n<p>It is a close cousin of mechanical <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/what-is-friction\/\">friction<\/a>, and the parallel runs deep: both oppose motion, both convert organised energy into heat, and neither is a force you can ever quite switch off.<\/p>\n\n<p>Two consequences fall straight out of this picture. Heat the lattice and collisions multiply, so resistance rises. Lengthen the obstacle course and there are more collisions to survive, so resistance rises again \u2014 exactly as R = \u03c1L\/A predicted.<\/p>\n\n<p>Then there is the exception that proves how strange nature can be. Cool certain materials below a critical temperature and resistance does not merely fall \u2014 it vanishes, completely, and a current once started will circulate for years without a battery.<\/p>\n\n<h2>Real-World Examples of Electrical Resistance<\/h2>\n\n<p>Resistance is not exam furniture. It is a design constraint that engineers wrestle with daily, and occasionally a safety feature that saves lives.<\/p>\n\n<h3>1. The toaster that glows<\/h3>\n\n<p>A toaster element is a long, thin nichrome ribbon \u2014 every term in R = \u03c1L\/A pushed deliberately in the direction of <em>more<\/em>. High \u03c1, big L, small A. The result is an element hot enough to brown bread while the copper flex behind it stays cool.<\/p>\n\n<h3>2. Why power lines run at 400,000 volts<\/h3>\n\n<p>Transmission losses go as I\u00b2R, so halving the current cuts losses fourfold. Since power is voltage times current, the trick is to send it at monstrous voltage and tiny current \u2014 which is precisely why pylons exist.<\/p>\n\n<h3>3. The cable that drops your voltage<\/h3>\n\n<p>Run 30 m of 2.5 mm\u00b2 copper to a garden workshop and the there-and-back conductor is 60 m \u2014 about 0.40 \u03a9. Draw 13 A through it and you lose over 5 V before the tool even starts. Worked problem 7 does the sum.<\/p>\n\n<h3>4. Thermometers with no mercury<\/h3>\n\n<p>Because resistance tracks temperature so predictably, you can run the logic backwards: measure R, infer T. Platinum resistance thermometers do exactly this, and the thermistor in your car&#8217;s coolant sensor is the cheap, twitchy cousin.<\/p>\n\n<h3>5. Why electricians respect wet hands<\/h3>\n\n<p>Dry skin can offer tens of thousands of ohms; wet skin, dramatically less. The mains voltage has not changed \u2014 but with R slashed, I = V\/R sends far more current through a body that was never designed to conduct it.<\/p>\n\n<figure style=\"margin:32px auto;max-width:640px;text-align:center;\">\n\n  <img decoding=\"async\" src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/07\/10-arden0010_1170_780_70_int_s_c1_huge-5fc34768.webp\"\n\n       alt=\"Glowing nichrome heating element demonstrating high electrical resistance converting current into heat\"\n\n       loading=\"lazy\"\n\n       style=\"width:100%;height:auto;border-radius:4px;\" \/>\n\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">Nichrome&#8217;s high resistivity turns electrical energy into heat and light, while the copper cable feeding it stays cool.<\/figcaption>\n\n<\/figure>\n\n<h2>Common Misconceptions About Electrical Resistance<\/h2>\n\n<h3>&#8220;Resistance and resistivity are the same thing&#8221;<\/h3>\n\n<p>They are not, and this is the single most common slip in the topic. Resistivity (\u03c1, in \u03a9\u00b7m) is a property of the <em>material<\/em>; resistance (R, in \u03a9) is a property of a particular <em>object<\/em> cut from it.<\/p>\n\n<p>Copper has one resistivity. A copper wire has a resistance that depends entirely on how you shaped it \u2014 and two wires from the same reel can differ by a factor of a thousand.<\/p>\n\n<h3>&#8220;A thicker wire has more resistance \u2014 there&#8217;s more metal in the way&#8221;<\/h3>\n\n<p>The opposite is true. More cross-sectional area means more parallel routes for charge, so resistance <em>falls<\/em>: R is proportional to 1\/A.<\/p>\n\n<p>Worse, the error usually hides a second one. Because A depends on d\u00b2, doubling the diameter quarters the resistance rather than halving it \u2014 a mistake that turns a correct method into a wrong answer.<\/p>\n\n<h3>&#8220;A resistor&#8217;s marked value is its resistance, full stop&#8221;<\/h3>\n\n<p>Only at the temperature it was specified at. Every metal resistor drifts with temperature, and components that get hot in normal use drift a lot.<\/p>\n\n<p>In practice this catches people out with lamps. A filament measures a few ohms cold on a multimeter and runs at ten to fifteen times that when lit \u2014 which is exactly why lamps blow at switch-on, when resistance is low and the inrush current is brutal.<\/p>\n\n<h2>How Electrical Resistance Relates to Current, Power and Circuits<\/h2>\n\n<p>Resistance connects to the rest of electricity through two equations you will use constantly. The first gives the current, the second gives the cost.<\/p>\n\n<div class=\"pf-formula\">P = I\u00b2R = V\u00b2 \/ R<\/div>\n\n<ul>\n<li><strong>P<\/strong> \u2014 power dissipated as heat, in watts (W)<\/li>\n<li><strong>I<\/strong> \u2014 current through the component, in amperes (A)<\/li>\n<li><strong>V<\/strong> \u2014 potential difference across it, in volts (V)<\/li>\n<li><strong>R<\/strong> \u2014 resistance, in ohms (\u03a9)<\/li>\n<\/ul>\n\n<p>Every ohm in a circuit is a tollbooth charging <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/what-is-energy-in-physics\/\">energy<\/a> as heat. Sometimes that is the entire product \u2014 a kettle, a toaster, a hair dryer. Usually it is pure waste, and the engineer&#8217;s job is to make R as small as economics allows.<\/p>\n\n<p>Combining resistors follows two rules. In <strong>series<\/strong> resistances add (R = R<sub>1<\/sub> + R<sub>2<\/sub> + \u2026), because you have lengthened the obstacle course. In <strong>parallel<\/strong> the reciprocals add (1\/R = 1\/R<sub>1<\/sub> + 1\/R<sub>2<\/sub> + \u2026), because you have widened it.<\/p>\n\n<p>That is not a coincidence \u2014 look again at R = \u03c1L\/A. Series is the L on top; parallel is the A underneath. Same formula, wearing a different hat.<\/p>\n\n<p>One habit worth stealing from working engineers: sanity-check the magnitude. Connecting wire should land near a hundredth of an ohm, a kettle element near twenty, your skin in the thousands. If a wire calculation gives you 400 \u03a9, the physics is fine \u2014 a unit conversion is not.<\/p>\n\n<h2>Worked Problems<\/h2>\n\n<p>Method beats answers. Write the formula, substitute with units, then solve \u2014 and convert to SI before anything else.<\/p>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 1<\/div><div class=\"pf-problem-question\">A component has a potential difference of 12 V across it and a current of 0.50 A flowing through it. What is its resistance?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\n\nStep 1: Resistance is defined as voltage over current, so use R = V \/ I.\n\nStep 2: Substitute with units: R = 12 V \u00f7 0.50 A.\n\nStep 3: Solve: R = 24 V\/A = 24 \u03a9.\n\n<strong>Answer: R = 24 \u03a9<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 2<\/div><div class=\"pf-problem-question\">A toaster element is made from 2.5 m of nichrome ribbon with a cross-sectional area of 0.20 mm\u00b2. Taking the resistivity of nichrome as 1.1 \u00d7 10^-6 \u03a9\u00b7m, find its resistance.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\n\nStep 1: Convert the area to SI first \u2014 this is where most marks are lost. A = 0.20 mm\u00b2 = 0.20 \u00d7 10<sup>\u22126<\/sup> m\u00b2 = 2.0 \u00d7 10<sup>\u22127<\/sup> m\u00b2.\n\nStep 2: Use R = \u03c1L \/ A and substitute: R = (1.1 \u00d7 10<sup>\u22126<\/sup> \u03a9\u00b7m \u00d7 2.5 m) \u00f7 (2.0 \u00d7 10<sup>\u22127<\/sup> m\u00b2).\n\nStep 3: Solve: R = 2.75 \u00d7 10<sup>\u22126<\/sup> \u00f7 2.0 \u00d7 10<sup>\u22127<\/sup> = 13.75 \u03a9 \u2248 14 \u03a9.\n\n<strong>Answer: R \u2248 14 \u03a9<\/strong> (a sensible element value \u2014 it would draw about 17 A at 230 V)\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 3<\/div><div class=\"pf-problem-question\">A wire has a resistance of 4.0 \u03a9. What is the resistance of a wire of the same material and length, but twice the diameter?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\n\nStep 1: R is inversely proportional to area A, and A = \u03c0d\u00b2\/4, so A depends on d\u00b2.\n\nStep 2: Doubling the diameter multiplies the area by 2\u00b2 = 4.\n\nStep 3: Since R is inversely proportional to A, the resistance is divided by 4: R = 4.0 \u03a9 \u00f7 4 = 1.0 \u03a9.\n\n<strong>Answer: R = 1.0 \u03a9<\/strong> (not 2.0 \u03a9 \u2014 the classic trap is halving instead of quartering)\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 4<\/div><div class=\"pf-problem-question\">A 1.5 m sample of wire with a cross-sectional area of 0.50 mm\u00b2 is measured to have a resistance of 0.048 \u03a9. What is the resistivity of the material, and what is it likely to be?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\n\nStep 1: Rearrange R = \u03c1L \/ A to make \u03c1 the subject: \u03c1 = RA \/ L.\n\nStep 2: Convert and substitute: A = 0.50 mm\u00b2 = 5.0 \u00d7 10<sup>\u22127<\/sup> m\u00b2, so \u03c1 = (0.048 \u03a9 \u00d7 5.0 \u00d7 10<sup>\u22127<\/sup> m\u00b2) \u00f7 1.5 m.\n\nStep 3: Solve: \u03c1 = 2.4 \u00d7 10<sup>\u22128<\/sup> \u00f7 1.5 = 1.6 \u00d7 10<sup>\u22128<\/sup> \u03a9\u00b7m.\n\n<strong>Answer: \u03c1 = 1.6 \u00d7 10<sup>\u22128<\/sup> \u03a9\u00b7m \u2014 consistent with copper (1.68 \u00d7 10<sup>\u22128<\/sup> \u03a9\u00b7m)<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 5<\/div><div class=\"pf-problem-question\">A copper motor winding has a resistance of 20.0 \u03a9 at 20 \u00b0C. The motor runs and the winding reaches 70 \u00b0C. Taking \u03b1 = 3.9 \u00d7 10^-3 per \u00b0C, find the new resistance.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\n\nStep 1: Use R = R<sub>0<\/sub>(1 + \u03b1\u0394T), with \u0394T measured from the reference temperature.\n\nStep 2: \u0394T = 70 \u00b0C \u2212 20 \u00b0C = 50 \u00b0C. Substitute: R = 20.0 \u03a9 \u00d7 (1 + 3.9 \u00d7 10<sup>\u22123<\/sup> \u00d7 50).\n\nStep 3: Solve: R = 20.0 \u00d7 (1 + 0.195) = 20.0 \u00d7 1.195 = 23.9 \u03a9.\n\n<strong>Answer: R = 23.9 \u03a9<\/strong> \u2014 a 20% rise from warming alone, which is why motor windings are rated hot, not cold\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 6<\/div><div class=\"pf-problem-question\">A metal wire is stretched until it is twice as long. Its volume stays constant. By what factor does its resistance change?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\n\nStep 1: Volume V = A \u00d7 L stays constant. If L doubles to 2L, then A must halve to A\/2.\n\nStep 2: Start from R = \u03c1L \/ A and substitute the new values: R<sub>new<\/sub> = \u03c1(2L) \u00f7 (A\/2).\n\nStep 3: Simplify: R<sub>new<\/sub> = 4 \u00d7 (\u03c1L \/ A) = 4R. Both changes push resistance the same way, so they multiply.\n\n<strong>Answer: The resistance becomes 4 times larger<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 7<\/div><div class=\"pf-problem-question\">A workshop is 30 m from a consumer unit, wired in 2.5 mm\u00b2 copper. A 13 A load is switched on. Find the cable resistance and the voltage lost in the cable. Take \u03c1 = 1.68 \u00d7 10^-8 \u03a9\u00b7m.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\n\nStep 1: Current must travel out and back, so the conductor length is L = 2 \u00d7 30 m = 60 m. Missing this halves your answer.\n\nStep 2: A = 2.5 mm\u00b2 = 2.5 \u00d7 10<sup>\u22126<\/sup> m\u00b2. Apply R = \u03c1L \/ A = (1.68 \u00d7 10<sup>\u22128<\/sup> \u00d7 60) \u00f7 (2.5 \u00d7 10<sup>\u22126<\/sup>) = 0.40 \u03a9.\n\nStep 3: Voltage lost in the cable: V = IR = 13 A \u00d7 0.40 \u03a9 = 5.2 V \u2014 about 2.3% of a 230 V supply, and heat the cable must shed.\n\n<strong>Answer: R \u2248 0.40 \u03a9, with about 5.2 V lost in the cable<\/strong>\n<\/div><\/details><\/div>\n\n<h2>Frequently Asked Questions<\/h2>\n\n<details class=\"pf-faq-item\"><summary>What is electrical resistance in simple terms?<\/summary><div class=\"pf-faq-item-answer\">\nElectrical resistance is how strongly something opposes electric current. It is the voltage across a component divided by the current through it (R = V\/I), measured in ohms. Think of water in a pipe: a narrow pipe resists flow and a wide one lets it through. A thin nichrome wire resists fiercely; a thick copper one barely at all.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the SI unit of electrical resistance?<\/summary><div class=\"pf-faq-item-answer\">\nThe SI unit of resistance is the ohm, symbol \u03a9, defined as one volt per ampere. A component has a resistance of 1 \u03a9 if 1 V drives 1 A through it. Larger values use kilohms (1 k\u03a9 = 1,000 \u03a9) and megohms (1 M\u03a9 = 1,000,000 \u03a9). The reciprocal, conductance, is measured in siemens.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What are the four factors affecting resistance?<\/summary><div class=\"pf-faq-item-answer\">\nResistance depends on the material&#8217;s resistivity, the conductor&#8217;s length, its cross-sectional area, and its temperature. The first three combine as R = \u03c1L\/A: resistance rises with length and falls with area. Temperature acts separately \u2014 for metals, hotter means more resistance, because the ion lattice vibrates harder and scatters electrons more often.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the difference between resistance and resistivity?<\/summary><div class=\"pf-faq-item-answer\">\nResistance belongs to an object; resistivity belongs to a material. Resistivity (\u03c1, in \u03a9\u00b7m) is fixed for a substance at a given temperature, whatever its shape. Resistance (R, in \u03a9) depends on that resistivity plus the object&#8217;s length and cross-sectional area, through R = \u03c1L\/A. Copper has one resistivity but a copper wire&#8217;s resistance depends on how it was drawn.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Does resistance increase with temperature?<\/summary><div class=\"pf-faq-item-answer\">\nFor metals, yes \u2014 resistance rises with temperature, roughly following R = R0(1 + \u03b1\u0394T). Copper gains about 0.39% per degree Celsius. Semiconductors do the reverse: heating frees more charge carriers, so their resistance falls. Superconductors are the extreme case, dropping to exactly zero resistance below a critical temperature.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Why does a longer wire have more resistance?<\/summary><div class=\"pf-faq-item-answer\">\nA longer wire has more resistance because electrons must travel further through the ion lattice and collide more often on the way. Resistance is directly proportional to length, so doubling the length doubles the resistance. Widening the wire does the opposite: more cross-sectional area gives charge more parallel routes, and resistance falls.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Can resistance ever be zero?<\/summary><div class=\"pf-faq-item-answer\">\nYes, but only in a superconductor. Cooled below its critical temperature, a superconductor loses all electrical resistance, and a current started in a loop will persist for years with no power source. Every ordinary conductor, including copper at room temperature, always has some resistance \u2014 which is why every real circuit warms up.\n<\/div><\/details>\n","protected":false},"excerpt":{"rendered":"<p>Electrical resistance measures how strongly a component opposes electric current: R = V\/I, measured in ohms. This guide covers the four factors behind R = \u03c1L\/A, the resistance-versus-resistivity trap, seven worked problems and an interactive lab.<\/p>\n","protected":false},"author":1,"featured_media":570,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-569","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-electromagnetism"],"_links":{"self":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/569","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/comments?post=569"}],"version-history":[{"count":1,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/569\/revisions"}],"predecessor-version":[{"id":578,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/569\/revisions\/578"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media\/570"}],"wp:attachment":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media?parent=569"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/categories?post=569"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/tags?post=569"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}