{"id":304,"date":"2026-06-23T01:49:10","date_gmt":"2026-06-23T01:49:10","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=304"},"modified":"2026-06-23T02:01:09","modified_gmt":"2026-06-23T02:01:09","slug":"series-parallel-circuits","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/series-parallel-circuits\/","title":{"rendered":"Series and Parallel Circuits Explained"},"content":{"rendered":"\n<div class=\"pf-citation\"><div class=\"eyebrow\">Definition<\/div><p>\nSeries and parallel circuits are the two basic ways to connect components in an electrical circuit. In a series circuit, components sit on a single current path, so the same current flows through each one and their voltages add up. In a parallel circuit, components share the same voltage across separate branches, and their currents add up.\n<\/p><\/div>\n\n<p>Flip one switch in your house and the other lights stay on. Pull a single bulb from an old string of fairy lights and the whole strand goes dark. Same electricity, completely different behaviour \u2014 and the only thing that changed is <em>how the parts are wired together<\/em>.<\/p>\n\n<p>That wiring choice sits at the heart of every circuit you will ever build or fix. Get it right and you can share a voltage, limit a current, or keep devices independent. Get it wrong and nothing lights up. This guide shows exactly how each arrangement behaves, with original diagrams, formulas, and eight worked examples.<\/p>\n\n<h2>What Are Series and Parallel Circuits?<\/h2>\n\n<p>Picture a single-lane road next to a motorway with several lanes. On the single lane, every car follows the one in front \u2014 that is a <strong>series circuit<\/strong>. On the motorway, traffic spreads across lanes and travels side by side \u2014 that is a <strong>parallel circuit<\/strong>.<\/p>\n\n<p>More precisely, a series circuit connects components end to end in one continuous loop, leaving a single path for current. A parallel circuit connects components across the same two points, giving the current two or more separate branches to flow through.<\/p>\n\n<p>This one structural choice decides three things at once: how the current splits, how the voltage divides, and what happens when a component fails. Everything else below follows from those three rules.<\/p>\n\n<svg viewBox=\"0 0 760 380\" role=\"img\" aria-label=\"Side-by-side schematics of a series circuit with one current path and a parallel circuit with three branches\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">\n  <rect x=\"0\" y=\"0\" width=\"760\" height=\"380\" fill=\"#FAF6EE\"><\/rect>\n  <line x1=\"380\" y1=\"30\" x2=\"380\" y2=\"352\" stroke=\"#D9CFB8\" stroke-width=\"2\" stroke-dasharray=\"4 6\"><\/line>\n\n  <text x=\"190\" y=\"46\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"20\" font-weight=\"700\" fill=\"#0A1628\">Series circuit<\/text>\n  <text x=\"190\" y=\"68\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#7A1F2B\">One path \u2014 current is the same everywhere<\/text>\n\n  <line x1=\"80\" y1=\"120\" x2=\"300\" y2=\"120\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"300\" y1=\"120\" x2=\"300\" y2=\"290\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"80\" y1=\"290\" x2=\"300\" y2=\"290\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"80\" y1=\"120\" x2=\"80\" y2=\"160\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"80\" y1=\"200\" x2=\"80\" y2=\"290\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n\n  <line x1=\"62\" y1=\"168\" x2=\"98\" y2=\"168\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"72\" y1=\"184\" x2=\"88\" y2=\"184\" stroke=\"#0A1628\" stroke-width=\"6\"><\/line>\n  <text x=\"48\" y=\"173\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"16\" font-weight=\"700\" fill=\"#7A1F2B\">+<\/text>\n\n  <rect x=\"110\" y=\"108\" width=\"40\" height=\"24\" rx=\"3\" fill=\"#C8932A\" stroke=\"#0A1628\" stroke-width=\"2\"><\/rect>\n  <text x=\"130\" y=\"100\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#0A1628\">R\u2081<\/text>\n  <rect x=\"170\" y=\"108\" width=\"40\" height=\"24\" rx=\"3\" fill=\"#C8932A\" stroke=\"#0A1628\" stroke-width=\"2\"><\/rect>\n  <text x=\"190\" y=\"100\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#0A1628\">R\u2082<\/text>\n  <rect x=\"230\" y=\"108\" width=\"40\" height=\"24\" rx=\"3\" fill=\"#C8932A\" stroke=\"#0A1628\" stroke-width=\"2\"><\/rect>\n  <text x=\"250\" y=\"100\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#0A1628\">R\u2083<\/text>\n\n  <polygon points=\"166,290 180,284 180,296\" fill=\"#7A1F2B\"><\/polygon>\n  <text x=\"200\" y=\"312\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"12\" fill=\"#142139\">current I (one loop)<\/text>\n\n  <text x=\"570\" y=\"46\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"20\" font-weight=\"700\" fill=\"#0A1628\">Parallel circuit<\/text>\n  <text x=\"570\" y=\"68\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#7A1F2B\">Many paths \u2014 voltage is the same across each<\/text>\n\n  <line x1=\"460\" y1=\"120\" x2=\"460\" y2=\"160\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"460\" y1=\"200\" x2=\"460\" y2=\"290\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"442\" y1=\"168\" x2=\"478\" y2=\"168\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"452\" y1=\"184\" x2=\"468\" y2=\"184\" stroke=\"#0A1628\" stroke-width=\"6\"><\/line>\n  <text x=\"428\" y=\"173\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"16\" font-weight=\"700\" fill=\"#7A1F2B\">+<\/text>\n\n  <line x1=\"460\" y1=\"120\" x2=\"690\" y2=\"120\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"460\" y1=\"290\" x2=\"690\" y2=\"290\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n\n  <line x1=\"520\" y1=\"120\" x2=\"520\" y2=\"150\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <rect x=\"508\" y=\"150\" width=\"24\" height=\"110\" rx=\"3\" fill=\"#C8932A\" stroke=\"#0A1628\" stroke-width=\"2\"><\/rect>\n  <line x1=\"520\" y1=\"260\" x2=\"520\" y2=\"290\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <text x=\"544\" y=\"209\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#0A1628\">R\u2081<\/text>\n\n  <line x1=\"590\" y1=\"120\" x2=\"590\" y2=\"150\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <rect x=\"578\" y=\"150\" width=\"24\" height=\"110\" rx=\"3\" fill=\"#C8932A\" stroke=\"#0A1628\" stroke-width=\"2\"><\/rect>\n  <line x1=\"590\" y1=\"260\" x2=\"590\" y2=\"290\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <text x=\"614\" y=\"209\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#0A1628\">R\u2082<\/text>\n\n  <line x1=\"660\" y1=\"120\" x2=\"660\" y2=\"150\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <rect x=\"648\" y=\"150\" width=\"24\" height=\"110\" rx=\"3\" fill=\"#C8932A\" stroke=\"#0A1628\" stroke-width=\"2\"><\/rect>\n  <line x1=\"660\" y1=\"260\" x2=\"660\" y2=\"290\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <text x=\"684\" y=\"209\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#0A1628\">R\u2083<\/text>\n\n  <text x=\"570\" y=\"312\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"12\" fill=\"#142139\">current splits: I = I\u2081 + I\u2082 + I\u2083<\/text>\n<\/svg>\n<p style=\"text-align:center;font-size:13px;color:#142139;font-style:italic;margin-top:6px;\">Figure 1: The same three resistors wired in series (one loop) and in parallel (three branches).<\/p>\n\n<h3>The single rule that defines each<\/h3>\n\n<p>In a <strong>series<\/strong> circuit there is only one path, so the current has nowhere else to go \u2014 it is identical through every component. In a <strong>parallel<\/strong> circuit every branch connects to the same two nodes, so each branch feels the same voltage.<\/p>\n\n<p>Hold onto one line and the rest is bookkeeping: <em>series shares current, parallel shares voltage<\/em>. The two cases are mirror images \u2014 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Series_and_parallel_circuits\" target=\"_blank\" rel=\"noopener\">voltage and current simply swap roles<\/a> between them.<\/p>\n\n<h2>The Series and Parallel Circuit Formulas<\/h2>\n\n<p>All of the maths rests on a single relationship \u2014 <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/ohms-law\/\">Ohm&#8217;s law<\/a> \u2014 which ties voltage, current, and resistance together.<\/p>\n\n<div class=\"pf-formula\">V = I \u00d7 R<\/div>\n\n<ul>\n<li><strong>V<\/strong> \u2014 voltage (potential difference), measured in volts (V)<\/li>\n<li><strong>I<\/strong> \u2014 current, measured in amperes (A)<\/li>\n<li><strong>R<\/strong> \u2014 resistance, measured in ohms (\u03a9)<\/li>\n<\/ul>\n\n<p>From here, the two circuit types differ only in how you combine the resistances.<\/p>\n\n<h3>Total resistance in series<\/h3>\n\n<p>Resistors in series simply add. Each one blocks the current one after another, so the obstacles stack up.<\/p>\n\n<div class=\"pf-formula\">R_total = R\u2081 + R\u2082 + R\u2083 + \u2026<\/div>\n\n<p>Adding any resistor in series always <em>increases<\/em> the total resistance.<\/p>\n\n<h3>Total resistance in parallel<\/h3>\n\n<p>Resistors in parallel combine through their reciprocals, because each extra branch gives current a new route \u2014 making it <em>easier<\/em>, not harder, for charge to flow.<\/p>\n\n<div class=\"pf-formula\">1 \/ R_total = 1\/R\u2081 + 1\/R\u2082 + 1\/R\u2083 + \u2026<\/div>\n\n<p>For two resistors, a shortcut avoids the fractions entirely:<\/p>\n\n<div class=\"pf-formula\">R_total = (R\u2081 \u00d7 R\u2082) \/ (R\u2081 + R\u2082)<\/div>\n\n<p>The answer is always <strong>smaller than the smallest<\/strong> resistor in the group. That is a fast sanity check \u2014 if your parallel total comes out bigger than a branch, you have slipped somewhere.<\/p>\n\n<h3>Power in any circuit<\/h3>\n\n<p>However the parts are wired, the power each component dissipates comes from the same trio of equations:<\/p>\n\n<div class=\"pf-formula\">P = V \u00d7 I = I\u00b2 \u00d7 R = V\u00b2 \/ R<\/div>\n\n<ul>\n<li><strong>P<\/strong> \u2014 power, measured in watts (W)<\/li>\n<\/ul>\n\n<p>In practice this hides a neat twist. In series the <em>largest<\/em> resistor turns the most energy to heat, because the current is shared and P = I\u00b2R favours big R. In parallel the <em>smallest<\/em> resistor dissipates the most, because the voltage is shared and P = V\u00b2\/R favours small R.<\/p>\n\n<p>Need a number fast? Drop your values into our <a href=\"https:\/\/physicsfundamentalsinfo.com\/calculators\/resistor\">Resistor Calculator<\/a> to get the total series or parallel resistance instantly, then check it against the worked examples below.<\/p>\n\n<h2>How Series and Parallel Circuits Work<\/h2>\n\n<p>Start with series. The battery pushes charge around a single loop, so whatever current leaves the battery must pass through every component and return unchanged. There is no junction for it to split at.<\/p>\n\n<p>Because each component resists that shared current, each one claims a slice of the battery&#8217;s voltage. Add the slices and you recover the full supply voltage \u2014 Kirchhoff&#8217;s voltage law, stated in plain English.<\/p>\n\n<div class=\"pf-formula\">V_supply = V\u2081 + V\u2082 + V\u2083 + \u2026<\/div>\n\n<p>So in series the current is shared and the voltage is divided. The bigger a resistor, the bigger its share of that voltage.<\/p>\n\n<h3>Why parallel behaves the opposite way<\/h3>\n\n<p>In parallel, every branch is wired straight across the battery&#8217;s two terminals. Each branch therefore sees the <strong>full supply voltage<\/strong>, exactly as if the others were not there.<\/p>\n\n<p>The current is what splits. Each branch draws its own current set by its resistance, and those branch currents add up to the total leaving the battery.<\/p>\n\n<div class=\"pf-formula\">I_total = I\u2081 + I\u2082 + I\u2083 + \u2026<\/div>\n\n<p>A low-resistance branch is a wide-open door and grabs a large current; a high-resistance branch barely sips. That is why parallel current divides <em>inversely<\/em> with resistance.<\/p>\n\n<h3>Combination circuits<\/h3>\n\n<p>Real circuits usually mix both arrangements. The trick is to reduce them in stages: collapse each parallel group into one equivalent resistor, then add up everything that is now in series.<\/p>\n\n<p>Work from the inside out, one block at a time, until a single resistance remains. For longer multi-step examples, the open-access <a href=\"https:\/\/phys.libretexts.org\/Bookshelves\/University_Physics\/University_Physics_(OpenStax)\/University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)\/10:_Direct-Current_Circuits\/10.03:_Resistors_in_Series_and_Parallel\" target=\"_blank\" rel=\"noopener\">University Physics<\/a> chapter on resistors in series and parallel is a thorough reference. The diagram below shows the idea on a simple three-resistor network.<\/p>\n\n<svg viewBox=\"0 0 720 300\" role=\"img\" aria-label=\"A combination circuit with a 4 ohm resistor in series with a 6 ohm and 3 ohm resistor in parallel\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">\n  <rect x=\"0\" y=\"0\" width=\"720\" height=\"300\" fill=\"#FAF6EE\"><\/rect>\n  <text x=\"360\" y=\"36\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"18\" font-weight=\"700\" fill=\"#0A1628\">Combination circuit: R\u2081 in series with R\u2082 \u2225 R\u2083<\/text>\n\n  <line x1=\"90\" y1=\"70\" x2=\"90\" y2=\"150\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"90\" y1=\"164\" x2=\"90\" y2=\"250\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"72\" y1=\"150\" x2=\"108\" y2=\"150\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"82\" y1=\"164\" x2=\"98\" y2=\"164\" stroke=\"#0A1628\" stroke-width=\"6\"><\/line>\n  <text x=\"60\" y=\"155\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"16\" font-weight=\"700\" fill=\"#7A1F2B\">+<\/text>\n  <text x=\"60\" y=\"120\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"12\" fill=\"#142139\">12 V<\/text>\n\n  <line x1=\"90\" y1=\"70\" x2=\"260\" y2=\"70\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <rect x=\"155\" y=\"58\" width=\"40\" height=\"24\" rx=\"3\" fill=\"#C8932A\" stroke=\"#0A1628\" stroke-width=\"2\"><\/rect>\n  <text x=\"175\" y=\"50\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#0A1628\">R\u2081 = 4 \u03a9<\/text>\n\n  <line x1=\"260\" y1=\"70\" x2=\"260\" y2=\"230\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"480\" y1=\"70\" x2=\"480\" y2=\"250\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <line x1=\"480\" y1=\"250\" x2=\"90\" y2=\"250\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n\n  <line x1=\"260\" y1=\"110\" x2=\"480\" y2=\"110\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <rect x=\"330\" y=\"98\" width=\"44\" height=\"24\" rx=\"3\" fill=\"#C8932A\" stroke=\"#0A1628\" stroke-width=\"2\"><\/rect>\n  <text x=\"352\" y=\"92\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#0A1628\">R\u2082 = 6 \u03a9<\/text>\n\n  <line x1=\"260\" y1=\"190\" x2=\"480\" y2=\"190\" stroke=\"#0A1628\" stroke-width=\"3\"><\/line>\n  <rect x=\"330\" y=\"178\" width=\"44\" height=\"24\" rx=\"3\" fill=\"#C8932A\" stroke=\"#0A1628\" stroke-width=\"2\"><\/rect>\n  <text x=\"352\" y=\"224\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#0A1628\">R\u2083 = 3 \u03a9<\/text>\n\n  <text x=\"560\" y=\"120\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#7A1F2B\">Step 1: 6 \u2225 3 = 2 \u03a9<\/text>\n  <text x=\"560\" y=\"150\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#7A1F2B\">Step 2: 4 + 2 = 6 \u03a9<\/text>\n  <text x=\"560\" y=\"180\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#142139\">Step 3: I = 12 \/ 6 = 2 A<\/text>\n<\/svg>\n<p style=\"text-align:center;font-size:13px;color:#142139;font-style:italic;margin-top:6px;\">Figure 2: Reduce the parallel pair first, then add the series resistor \u2014 a single 6 \u03a9 equivalent remains.<\/p>\n\n<div class=\"pf-sim-slot\"><div class=\"pf-sim-slot-header\"><span class=\"icon-dot\"><\/span><span class=\"label\">Series and Parallel Circuits 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\/series-parallel-circuits.html?embed=1\" class=\"pf-sim-frame\" loading=\"lazy\"><\/iframe><\/div><\/div>\n\n<h2>Series vs Parallel Circuits: 7 Key Differences<\/h2>\n\n<p>The table below sums up everything that changes when you switch a circuit from series to parallel. Master these seven contrasts and you can predict how almost any simple circuit will behave.<\/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;\">Feature<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Series circuit<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Parallel circuit<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Current paths<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">One single loop<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Two or more branches<\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Current<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Same through every component<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Splits between branches (I = I\u2081 + I\u2082 + \u2026)<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Voltage<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Divides across components (V = V\u2081 + V\u2082 + \u2026)<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Same full voltage across each branch<\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Total resistance<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Adds up: R\u2081 + R\u2082 + \u2026<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Reciprocal sum; less than the smallest resistor<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Adding a resistor<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Total resistance rises<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Total resistance falls<\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>If one component fails (open)<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Whole circuit stops<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Other branches keep working<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Common uses<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Voltage dividers, current-limiting, older fairy lights<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Mains\/house wiring, appliances, car electrics<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<h2>Real-World Examples of Series and Parallel Circuits<\/h2>\n\n<p>These arrangements are not textbook abstractions \u2014 you are surrounded by both right now. Here are five places the choice shows up.<\/p>\n\n<h3>1. Household wiring (parallel)<\/h3>\n\n<p>Every socket and light in your home sits in parallel across the mains. That is why each one gets the same voltage \u2014 about 230 V in the UK and Europe, 120 V in North America \u2014 and why switching off the kettle never dims the lamps.<\/p>\n\n<h3>2. Fairy lights and the classic &#8220;one out, all out&#8221; (series)<\/h3>\n\n<p>Older string lights wired their bulbs in series. Lovely when they worked, maddening when they did not \u2014 a single broken filament opened the loop and killed the whole strand.<\/p>\n\n<p>Modern LED strings dodge this with tiny shunts or parallel sections, so one dead lamp no longer drags the rest down with it.<\/p>\n\n<figure style=\"margin:32px auto;max-width:640px;text-align:center;\">\n  <img decoding=\"async\" src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/06\/71nolh8hfDL.jpg\" alt=\"String of fairy lights wired as a series circuit\" loading=\"lazy\" style=\"width:100%;height:auto;border-radius:4px;\">\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">Older fairy lights wire their bulbs in series \u2014 one failure can darken the whole strand.<\/figcaption>\n<\/figure>\n\n<h3>3. Car headlights and electronics (parallel)<\/h3>\n\n<p>A car wires its lamps and modules in parallel, so one can fail without blacking out the others and each still receives the full 12 V from the battery.<\/p>\n\n<h3>4. Battery packs (series and parallel)<\/h3>\n\n<p>Stack cells in series and their voltages add \u2014 four 1.5 V AA cells in a row give 6 V. Wire identical cells in parallel instead and the voltage stays put while the pack delivers more current for longer.<\/p>\n\n<h3>5. Voltage dividers (series)<\/h3>\n\n<p>Two resistors in series split a voltage in a fixed ratio. This humble series trick sets reference voltages, scales sensor signals, and sits inside countless volume knobs and dimmers.<\/p>\n\n<h2>Common Misconceptions About Series and Parallel Circuits<\/h2>\n\n<p>A few sticky beliefs trip up almost everyone learning this topic. Clear these and the rest clicks into place.<\/p>\n\n<h3>&#8220;Current gets used up as it flows&#8221;<\/h3>\n\n<p>It does not. Charge is conserved \u2014 the current returning to the battery equals the current that left it. What the components consume is <em>energy<\/em>, not current. In series, the same amperage flows at every point in the loop.<\/p>\n\n<h3>&#8220;Adding resistors always increases resistance&#8221;<\/h3>\n\n<p>True for series, false for parallel. Each parallel resistor opens a fresh path, so the total resistance drops below the smallest branch. More routes mean less overall opposition.<\/p>\n\n<h3>&#8220;Every branch in a parallel circuit carries the same current&#8221;<\/h3>\n\n<p>It is the <strong>voltage<\/strong> that is shared in parallel, not the current. Branch currents depend on resistance \u2014 the smaller the resistance, the larger its share.<\/p>\n\n<h3>&#8220;A bigger resistor always means a bigger voltage drop&#8221;<\/h3>\n\n<p>Only when components share the same current, which is the series case. In parallel, every branch already sits at the same voltage, so a bigger resistor just means a smaller current, not a bigger drop.<\/p>\n\n<h2>How Series and Parallel Circuits Relate to Charge and Energy<\/h2>\n\n<p>Every result on this page is Ohm&#8217;s law wearing different clothes. Get fluent with that one relationship and the series and parallel rules stop being something to memorise \u2014 you can derive them on the spot.<\/p>\n\n<p>Underneath the current, what actually moves is electric charge. The same electrostatic forces captured by <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/coulombs-law\/\">Coulomb&#8217;s law<\/a> are what nudge electrons through each resistor, whichever way the circuit is wired.<\/p>\n\n<p>Resistors destroy nothing \u2014 they convert electrical <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/what-is-energy-in-physics\/\">energy<\/a> into heat and light. The rate of that conversion is power, which is simply the <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/work-done-in-physics\/\">work done<\/a> by the battery each second as it drives charge around the loop.<\/p>\n\n<h2>Worked Problems<\/h2>\n\n<p>Eight problems, building from a single addition to a reverse calculation. Try each before reading the solution \u2014 and watch the units the whole way through.<\/p>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 1<\/div><div class=\"pf-problem-question\">Three resistors of 2 \u03a9, 4 \u03a9 and 6 \u03a9 are connected in series. What is the total resistance?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: For a series circuit, resistances add \u2014 R_total = R\u2081 + R\u2082 + R\u2083.\nStep 2: Substitute the values \u2014 R_total = 2 \u03a9 + 4 \u03a9 + 6 \u03a9.\nStep 3: Add \u2014 R_total = 12 \u03a9.\n<strong>Answer: R_total = 12 \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 6 \u03a9 resistor and a 12 \u03a9 resistor are connected in parallel. What is their total resistance?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: For two resistors in parallel, use R_total = (R\u2081 \u00d7 R\u2082) \/ (R\u2081 + R\u2082).\nStep 2: Substitute \u2014 R_total = (6 \u00d7 12) \/ (6 + 12) = 72 \/ 18.\nStep 3: Divide \u2014 R_total = 4 \u03a9, which is smaller than the 6 \u03a9 branch, exactly as expected.\n<strong>Answer: R_total = 4 \u03a9<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 3<\/div><div class=\"pf-problem-question\">A 12 V battery drives a 3 \u03a9 resistor and a 5 \u03a9 resistor in series. Find the current and the voltage across each resistor.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: Total resistance \u2014 R_total = 3 \u03a9 + 5 \u03a9 = 8 \u03a9.\nStep 2: Current from Ohm&#8217;s law \u2014 I = V \/ R = 12 V \/ 8 \u03a9 = 1.5 A, the same through both.\nStep 3: Voltage across each \u2014 V\u2081 = I \u00d7 R\u2081 = 1.5 \u00d7 3 = 4.5 V; V\u2082 = I \u00d7 R\u2082 = 1.5 \u00d7 5 = 7.5 V. Check: 4.5 + 7.5 = 12 V.\n<strong>Answer: I = 1.5 A, V\u2081 = 4.5 V, V\u2082 = 7.5 V<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 4<\/div><div class=\"pf-problem-question\">A 24 V supply is connected across an 8 \u03a9 resistor and a 12 \u03a9 resistor in parallel. Find the current in each branch and the total current.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: Each branch sees the full 24 V, so apply Ohm&#8217;s law per branch \u2014 I = V \/ R.\nStep 2: I\u2081 = 24 \/ 8 = 3 A; I\u2082 = 24 \/ 12 = 2 A.\nStep 3: Total current is the sum of the branches \u2014 I_total = 3 + 2 = 5 A.\n<strong>Answer: I\u2081 = 3 A, I\u2082 = 2 A, I_total = 5 A<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 5<\/div><div class=\"pf-problem-question\">Three identical 30 \u03a9 resistors are connected in parallel. What is the total resistance?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: For n identical resistors in parallel, R_total = R \/ n.\nStep 2: Substitute \u2014 R_total = 30 \u03a9 \/ 3.\nStep 3: Divide \u2014 R_total = 10 \u03a9. Reciprocal check: 1\/R = 1\/30 + 1\/30 + 1\/30 = 3\/30 = 1\/10.\n<strong>Answer: R_total = 10 \u03a9<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 6<\/div><div class=\"pf-problem-question\">A 4 \u03a9 resistor is in series with a parallel pair of 6 \u03a9 and 3 \u03a9, all across a 12 V battery. Find the equivalent resistance and the total current.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: Reduce the parallel pair first \u2014 R_p = (6 \u00d7 3) \/ (6 + 3) = 18 \/ 9 = 2 \u03a9.\nStep 2: Add the series resistor \u2014 R_total = 4 \u03a9 + 2 \u03a9 = 6 \u03a9.\nStep 3: Total current from Ohm&#8217;s law \u2014 I = V \/ R = 12 \/ 6 = 2 A.\n<strong>Answer: R_total = 6 \u03a9, I = 2 A<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 7<\/div><div class=\"pf-problem-question\">Two 100 \u03a9 resistors are connected in series across a 20 V supply. Find the total power dissipated and the power in each resistor.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: Total resistance \u2014 R_total = 100 + 100 = 200 \u03a9; current I = V \/ R = 20 \/ 200 = 0.1 A.\nStep 2: Total power \u2014 P = V \u00d7 I = 20 \u00d7 0.1 = 2 W.\nStep 3: Each resistor \u2014 P = I\u00b2 \u00d7 R = (0.1)\u00b2 \u00d7 100 = 1 W. Check: 1 W + 1 W = 2 W.\n<strong>Answer: P_total = 2 W; 1 W in each resistor<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 8<\/div><div class=\"pf-problem-question\">Two resistors in parallel give a total resistance of 4 \u03a9. If one of them is 6 \u03a9, find the other.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: Start from 1\/R_total = 1\/R\u2081 + 1\/R\u2082, so 1\/R\u2082 = 1\/R_total \u2212 1\/R\u2081.\nStep 2: Substitute \u2014 1\/R\u2082 = 1\/4 \u2212 1\/6 = 3\/12 \u2212 2\/12 = 1\/12.\nStep 3: Invert \u2014 R\u2082 = 12 \u03a9. Check: (6 \u00d7 12) \/ (6 + 12) = 72 \/ 18 = 4 \u03a9.\n<strong>Answer: R\u2082 = 12 \u03a9<\/strong>\n<\/div><\/details><\/div>\n\n<h2>Frequently Asked Questions<\/h2>\n\n<details class=\"pf-faq-item\"><summary>What is the main difference between series and parallel circuits?<\/summary><div class=\"pf-faq-item-answer\">\nIn a series circuit, components share one current path, so the same current flows through each and the voltage divides between them. In a parallel circuit, components sit on separate branches that share the same voltage, while the current divides between them. Series wiring adds resistance; parallel wiring reduces it below the smallest branch.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>How do you calculate total resistance in a parallel circuit?<\/summary><div class=\"pf-faq-item-answer\">\nAdd the reciprocals of each resistance, then take the reciprocal of the result: 1\/R_total = 1\/R\u2081 + 1\/R\u2082 + \u2026 For two resistors, use the shortcut R_total = (R\u2081 \u00d7 R\u2082) \/ (R\u2081 + R\u2082). The total is always smaller than the smallest resistor, which is a quick way to check your working.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Is voltage the same in series or parallel?<\/summary><div class=\"pf-faq-item-answer\">\nVoltage is the same across each branch in a parallel circuit, because every branch connects to the same two points. In a series circuit the voltage is divided instead \u2014 each component drops a share set by its resistance, and those shares add up to the full supply voltage.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Why are houses wired in parallel instead of series?<\/summary><div class=\"pf-faq-item-answer\">\nParallel wiring gives every socket the same full voltage and lets each appliance run independently. If a home were wired in series, switching off one device would break the loop and shut everything down, and each appliance would receive only a fraction of the mains voltage. Parallel keeps devices isolated, fully powered, and safer.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What happens if one bulb breaks in a series circuit?<\/summary><div class=\"pf-faq-item-answer\">\nThe whole circuit stops. A series circuit has a single path, so a broken bulb opens the loop and no current can flow anywhere \u2014 every other bulb goes dark too. This is the classic &#8220;one out, all out&#8221; problem of older fairy lights. In a parallel circuit, the remaining branches carry on working.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Are Christmas (fairy) lights series or parallel?<\/summary><div class=\"pf-faq-item-answer\">\nTraditional fairy lights were wired in series, which is why one failed bulb could darken the entire strand. Most modern LED string lights use shunts or parallel sections, so a single dead lamp no longer kills the rest. Some decorative sets still use short series groups so the bulbs can share the supply voltage.\n<\/div><\/details>\n","protected":false},"excerpt":{"rendered":"<p>A clear guide to series and parallel circuits \u2014 how current, voltage and resistance behave in each, with original diagrams, formulas and eight worked examples.<\/p>\n","protected":false},"author":1,"featured_media":306,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[159,157,83,155,158,156],"class_list":["post-304","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-electromagnetism","tag-combination-circuits","tag-electric-circuits","tag-ohms-law","tag-parallel-circuits","tag-resistors","tag-series-circuits"],"_links":{"self":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/304","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=304"}],"version-history":[{"count":2,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/304\/revisions"}],"predecessor-version":[{"id":309,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/304\/revisions\/309"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media\/306"}],"wp:attachment":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media?parent=304"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/categories?post=304"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/tags?post=304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}