{"id":677,"date":"2026-07-29T10:16:15","date_gmt":"2026-07-29T10:16:15","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=677"},"modified":"2026-07-29T10:22:03","modified_gmt":"2026-07-29T10:22:03","slug":"capacitance","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/capacitance\/","title":{"rendered":"What Is Capacitance? C = Q\/V and Energy Stored"},"content":{"rendered":"\n<div class=\"pf-citation\"><div class=\"eyebrow\">Definition<\/div><p>\n\nCapacitance is the amount of electric charge a component stores for every volt of potential difference across it, defined by C = Q\/V and measured in farads. One farad equals one coulomb per volt. A charged capacitor also stores energy equal to half the capacitance multiplied by the voltage squared.\n\n<\/p><\/div>\n\n<p>Press the shutter on a camera with a built-in flash and you sometimes hear a faint rising whine before it fires. That is a capacitor filling up. The battery cannot dump its energy fast enough to make a bright flash, so it trickles charge into a capacitor for a second or two, and the capacitor releases the lot in about a thousandth of a second.<\/p> <p>The numbers are worth sitting with. A typical AA cell holds roughly 10 kJ of energy; a camera flash capacitor holds around 9 J \u2014 about a thousand times less. Yet the capacitor wins, because it can hand that energy over thousands of times faster. Capacitance is the property that decides how much charge a component can park, and how much energy comes back out.<\/p> <h2>What Is Capacitance?<\/h2> <p>Capacitance is the charge a conductor stores for every volt applied to it, written C = Q\/V. A component with a large capacitance accepts a lot of charge without its voltage climbing much; a small one fills up almost immediately.<\/p> <p>Think of a spring. Push on a stiff spring and it barely moves; push on a floppy one and it travels a long way for the same force. Voltage is the push, stored charge is the movement, and capacitance is the floppiness \u2014 how much charge you get per volt of push.<\/p> <p>The precise definition depends slightly on what you are measuring:<\/p> <ul> <li><strong>An isolated conductor<\/strong> \u2014 C is the charge on it divided by its potential relative to a point infinitely far away.<\/li> <li><strong>A capacitor<\/strong> (two conductors separated by an insulator) \u2014 Q is the magnitude of the charge on <em>each<\/em> plate, and V is the potential difference between them.<\/li> <\/ul> <p>The second case is the one you meet in circuits, and it hides a subtlety worth flagging early. A &#8220;charged&#8221; capacitor holds +Q on one plate and -Q on the other, so its total charge is zero. It has not stored charge so much as pulled charge apart and held it there.<\/p> <h2>The Capacitance Formula: C = Q\/V<\/h2> <p>The defining formula for capacitance divides the charge stored on one plate by the potential difference across the capacitor.<\/p>\n\n<div class=\"pf-formula\">C = Q \/ V<\/div>\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;\"> <table style=\"width:100%;border-collapse:collapse;word-break:break-word;\"> <thead> <tr> <th style=\"border:1px solid #D9CFB8;padding:8px;text-align:left;\">Symbol<\/th> <th style=\"border:1px solid #D9CFB8;padding:8px;text-align:left;\">Quantity<\/th> <th style=\"border:1px solid #D9CFB8;padding:8px;text-align:left;\">SI unit<\/th> <\/tr> <\/thead> <tbody> <tr> <td style=\"border:1px solid #D9CFB8;padding:8px;\"><strong>C<\/strong><\/td> <td style=\"border:1px solid #D9CFB8;padding:8px;\">Capacitance<\/td> <td style=\"border:1px solid #D9CFB8;padding:8px;\">farad (F)<\/td> <\/tr> <tr> <td style=\"border:1px solid #D9CFB8;padding:8px;\"><strong>Q<\/strong><\/td> <td style=\"border:1px solid #D9CFB8;padding:8px;\">Charge stored on one plate<\/td> <td style=\"border:1px solid #D9CFB8;padding:8px;\">coulomb (C)<\/td> <\/tr> <tr> <td style=\"border:1px solid #D9CFB8;padding:8px;\"><strong>V<\/strong><\/td> <td style=\"border:1px solid #D9CFB8;padding:8px;\">Potential difference across the plates<\/td> <td style=\"border:1px solid #D9CFB8;padding:8px;\">volt (V)<\/td> <\/tr> <\/tbody> <\/table> <\/div> <p>Rearranged, the same relationship gives you <strong>Q = CV<\/strong> and <strong>V = Q\/C<\/strong>. If you want the arithmetic done for you while you check your own working, our <a href=\"https:\/\/physicsfundamentalsinfo.com\/calculators\/capacitance\">Capacitance Calculator<\/a> solves for capacitance, charge or voltage and returns the stored energy alongside.<\/p> <p>Here is the point that trips people up. Capacitance is <em>not<\/em> set by Q or V \u2014 it is fixed by the capacitor&#8217;s geometry and the insulator inside it. Double the voltage and you double the charge; the ratio between them does not budge.<\/p> <h3>The Parallel-Plate Formula<\/h3> <p>For the simplest capacitor \u2014 two flat plates facing each other \u2014 capacitance follows directly from the geometry:<\/p>\n\n<div class=\"pf-formula\">C = \u03b5<sub>0<\/sub>\u03b5<sub>r<\/sub>A \/ d<\/div>\n\n<ul> <li><strong>\u03b5<sub>0<\/sub><\/strong> \u2014 the vacuum permittivity, 8.854 \u00d7 10<sup>-12<\/sup> farads per metre (F\/m)<\/li> <li><strong>\u03b5<sub>r<\/sub><\/strong> \u2014 relative permittivity (dielectric constant) of the insulator, a dimensionless number<\/li> <li><strong>A<\/strong> \u2014 the overlapping area of one plate, in square metres (m<sup>2<\/sup>)<\/li> <li><strong>d<\/strong> \u2014 the separation between the plates, in metres (m)<\/li> <\/ul> <p>This formula assumes the plates are large compared with their spacing, so the field between them is uniform and edge effects are negligible. Real capacitors deviate slightly, but for teaching and for most design work it is accurate enough.<\/p> <figure style=\"margin:32px auto;max-width:700px;\"> <svg viewBox=\"0 0 700 400\" role=\"img\" aria-label=\"Diagram of a parallel plate capacitor showing charge Q on each plate, plate area A, separation d, the uniform electric field between the plates and the capacitance formula C equals Q over V\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:100%;height:auto;\"> <rect x=\"0\" y=\"0\" width=\"700\" height=\"400\" fill=\"#F5F2EA\"><\/rect> <defs> <marker id=\"pfArrow\" markerWidth=\"9\" markerHeight=\"9\" refX=\"8\" refY=\"3\" orient=\"auto\"><path d=\"M0,0 L8,3 L0,6 Z\" fill=\"#142139\"><\/path><\/marker> <marker id=\"pfDim\" markerWidth=\"9\" markerHeight=\"9\" refX=\"8\" refY=\"3\" orient=\"auto\"><path d=\"M0,0 L8,3 L0,6 Z\" fill=\"#7A1F2B\"><\/path><\/marker> <marker id=\"pfDimS\" markerWidth=\"9\" markerHeight=\"9\" refX=\"1\" refY=\"3\" orient=\"auto\"><path d=\"M8,0 L0,3 L8,6 Z\" fill=\"#7A1F2B\"><\/path><\/marker> <\/defs> <text x=\"350\" y=\"34\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"19\" fill=\"#0A1628\">Parallel-Plate Capacitor<\/text> <rect x=\"238\" y=\"80\" width=\"15\" height=\"190\" fill=\"#C8932A\"><\/rect> <rect x=\"447\" y=\"80\" width=\"15\" height=\"190\" fill=\"#7A1F2B\"><\/rect> <text x=\"245\" y=\"70\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"20\" fill=\"#C8932A\">+Q<\/text> <text x=\"455\" y=\"70\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"20\" fill=\"#7A1F2B\">-Q<\/text> <line x1=\"258\" y1=\"110\" x2=\"442\" y2=\"110\" stroke=\"#142139\" stroke-width=\"2\" marker-end=\"url(#pfArrow)\"><\/line> <line x1=\"258\" y1=\"150\" x2=\"442\" y2=\"150\" stroke=\"#142139\" stroke-width=\"2\" marker-end=\"url(#pfArrow)\"><\/line> <line x1=\"258\" y1=\"190\" x2=\"442\" y2=\"190\" stroke=\"#142139\" stroke-width=\"2\" marker-end=\"url(#pfArrow)\"><\/line> <line x1=\"258\" y1=\"230\" x2=\"442\" y2=\"230\" stroke=\"#142139\" stroke-width=\"2\" marker-end=\"url(#pfArrow)\"><\/line> <text x=\"350\" y=\"172\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"17\" fill=\"#142139\">E<\/text> <line x1=\"238\" y1=\"292\" x2=\"462\" y2=\"292\" stroke=\"#7A1F2B\" stroke-width=\"1.5\" marker-start=\"url(#pfDimS)\" marker-end=\"url(#pfDim)\"><\/line> <text x=\"350\" y=\"312\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"16\" fill=\"#7A1F2B\">separation d<\/text> <line x1=\"205\" y1=\"80\" x2=\"205\" y2=\"270\" stroke=\"#7A1F2B\" stroke-width=\"1.5\" marker-start=\"url(#pfDimS)\" marker-end=\"url(#pfDim)\"><\/line> <text x=\"196\" y=\"180\" text-anchor=\"end\" font-family=\"Georgia,serif\" font-size=\"16\" fill=\"#7A1F2B\">plate<\/text> <text x=\"196\" y=\"200\" text-anchor=\"end\" font-family=\"Georgia,serif\" font-size=\"16\" fill=\"#7A1F2B\">area A<\/text> <line x1=\"245\" y1=\"270\" x2=\"245\" y2=\"345\" stroke=\"#142139\" stroke-width=\"2\"><\/line> <line x1=\"455\" y1=\"270\" x2=\"455\" y2=\"345\" stroke=\"#142139\" stroke-width=\"2\"><\/line> <line x1=\"245\" y1=\"345\" x2=\"330\" y2=\"345\" stroke=\"#142139\" stroke-width=\"2\"><\/line> <line x1=\"370\" y1=\"345\" x2=\"455\" y2=\"345\" stroke=\"#142139\" stroke-width=\"2\"><\/line> <line x1=\"330\" y1=\"330\" x2=\"330\" y2=\"360\" stroke=\"#142139\" stroke-width=\"3\"><\/line> <line x1=\"370\" y1=\"337\" x2=\"370\" y2=\"353\" stroke=\"#142139\" stroke-width=\"6\"><\/line> <text x=\"350\" y=\"382\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"16\" fill=\"#142139\">supply, voltage V<\/text> <text x=\"580\" y=\"150\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"22\" fill=\"#0A1628\">C = Q \/ V<\/text> <line x1=\"512\" y1=\"168\" x2=\"648\" y2=\"168\" stroke=\"#C8932A\" stroke-width=\"2\"><\/line> <text x=\"580\" y=\"198\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"15\" fill=\"#142139\">capacitance =<\/text> <text x=\"580\" y=\"220\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"15\" fill=\"#142139\">charge per volt<\/text> <\/svg> <p style=\"text-align:center;font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">Capacitance of a parallel-plate capacitor depends on plate area, separation and the insulator between the plates.<\/p> <\/figure> <h2>How Much Energy Does a Capacitor Store?<\/h2> <p>A charged capacitor stores energy equal to half the charge times the voltage \u2014 not the full QV. The same quantity can be written three equivalent ways, and which one you reach for depends on what you already know.<\/p>\n\n<div class=\"pf-formula\">U = \u00bdCV\u00b2 = \u00bdQV = Q\u00b2 \/ (2C)<\/div>\n\n<ul> <li><strong>U<\/strong> \u2014 energy stored, in joules (J)<\/li> <li><strong>C<\/strong> \u2014 capacitance, in farads (F)<\/li> <li><strong>V<\/strong> \u2014 potential difference across the capacitor, in volts (V)<\/li> <li><strong>Q<\/strong> \u2014 charge on one plate, in coulombs (C)<\/li> <\/ul> <h3>Where the Half Comes From<\/h3> <p>Why half? Because the voltage is not constant while the capacitor charges \u2014 it climbs from zero to V as charge piles up.<\/p> <p>The very first packet of charge crosses an empty capacitor and does almost no work against the field. The last packet has to fight its way across the full voltage. Averaged over the whole process, each unit of charge crosses an average potential of V\/2, which is exactly where the factor of one half comes from.<\/p> <p>Formally, moving a small charge dq across the instantaneous voltage q\/C costs dW = (q\/C) dq. Integrating from 0 to Q gives U = Q\u00b2\/(2C), and substituting Q = CV recovers the other two forms.<\/p> <figure style=\"margin:32px auto;max-width:640px;\"> <svg viewBox=\"0 0 640 400\" role=\"img\" aria-label=\"Graph of voltage against charge for a capacitor, a straight line through the origin, with the shaded triangle underneath representing the energy stored equal to half Q V\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:100%;height:auto;\"> <rect x=\"0\" y=\"0\" width=\"640\" height=\"400\" fill=\"#F5F2EA\"><\/rect> <text x=\"320\" y=\"32\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"19\" fill=\"#0A1628\">Energy Stored Is the Area Under the V\u2013Q Line<\/text> <polygon points=\"100,320 480,320 480,90\" fill=\"#C8932A\" fill-opacity=\"0.35\"><\/polygon> <line x1=\"100\" y1=\"320\" x2=\"480\" y2=\"90\" stroke=\"#7A1F2B\" stroke-width=\"3\"><\/line> <line x1=\"100\" y1=\"60\" x2=\"100\" y2=\"320\" stroke=\"#142139\" stroke-width=\"2\"><\/line> <line x1=\"100\" y1=\"320\" x2=\"560\" y2=\"320\" stroke=\"#142139\" stroke-width=\"2\"><\/line> <line x1=\"480\" y1=\"320\" x2=\"480\" y2=\"90\" stroke=\"#142139\" stroke-width=\"1\" stroke-dasharray=\"4,4\"><\/line> <line x1=\"100\" y1=\"90\" x2=\"480\" y2=\"90\" stroke=\"#142139\" stroke-width=\"1\" stroke-dasharray=\"4,4\"><\/line> <text x=\"70\" y=\"96\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"16\" fill=\"#142139\">V<\/text> <text x=\"480\" y=\"344\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"16\" fill=\"#142139\">Q<\/text> <text x=\"88\" y=\"52\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"15\" fill=\"#142139\">voltage<\/text> <text x=\"556\" y=\"344\" text-anchor=\"end\" font-family=\"Georgia,serif\" font-size=\"15\" fill=\"#142139\">charge<\/text> <text x=\"290\" y=\"280\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"18\" fill=\"#0A1628\">area = \u00bdQV<\/text> <text x=\"290\" y=\"304\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"15\" fill=\"#142139\">= energy stored<\/text> <text x=\"330\" y=\"150\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"15\" fill=\"#7A1F2B\">slope = 1 \/ C<\/text> <text x=\"320\" y=\"380\" text-anchor=\"middle\" font-family=\"Georgia,serif\" font-size=\"15\" fill=\"#1F2E47\">The line is straight, so the area is a triangle \u2014 hence the factor of one half.<\/text> <\/svg> <p style=\"text-align:center;font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">Voltage rises in proportion to stored charge, so the energy is the triangular area under the line, not the full rectangle QV.<\/p> <\/figure> <p>A quick sanity check you can use in an exam: if you ever write U = QV, you have claimed the capacitor charged at full voltage from the very start. It did not.<\/p> <h2>What Changes a Capacitor&#8217;s Capacitance?<\/h2> <p>Three things set the capacitance of a parallel-plate capacitor: plate area, plate separation, and the insulating material between the plates. Each acts in a way you can reason out physically.<\/p> <ul> <li><strong>Larger plate area<\/strong> raises capacitance. More room for charge to spread out means less crowding, so less voltage builds up per unit of charge added.<\/li> <li><strong>Smaller separation<\/strong> raises capacitance. The opposite charges pull on each other more strongly across a narrow gap, holding more charge in place at the same voltage.<\/li> <li><strong>A dielectric<\/strong> raises capacitance. The insulator&#8217;s molecules polarise and partly cancel the field between the plates, so the voltage drops and C rises by the factor \u03b5<sub>r<\/sub>.<\/li> <\/ul> <p>That third effect is why real capacitors are not just two bits of metal in air. Choosing the right dielectric buys you a factor of thousands.<\/p> <div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\"> <table style=\"width:100%;border-collapse:collapse;word-break:break-word;\"> <thead> <tr> <th style=\"border:1px solid #D9CFB8;padding:8px;text-align:left;\">Material between the plates<\/th> <th style=\"border:1px solid #D9CFB8;padding:8px;text-align:left;\">Relative permittivity \u03b5<sub>r<\/sub> (approx.)<\/th> <th style=\"border:1px solid #D9CFB8;padding:8px;text-align:left;\">Effect on C<\/th> <\/tr> <\/thead> <tbody> <tr><td style=\"border:1px solid #D9CFB8;padding:8px;\">Vacuum<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">1 (exactly)<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">Baseline<\/td><\/tr> <tr><td style=\"border:1px solid #D9CFB8;padding:8px;\">Dry air<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">1.0006<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">Indistinguishable from vacuum<\/td><\/tr> <tr><td style=\"border:1px solid #D9CFB8;padding:8px;\">Paper<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">3.5<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">About 3.5\u00d7<\/td><\/tr> <tr><td style=\"border:1px solid #D9CFB8;padding:8px;\">Mica<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">5<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">About 5\u00d7<\/td><\/tr> <tr><td style=\"border:1px solid #D9CFB8;padding:8px;\">Water (20 \u00b0C)<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">80<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">About 80\u00d7<\/td><\/tr> <tr><td style=\"border:1px solid #D9CFB8;padding:8px;\">Barium titanate ceramic<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">1,000 and above<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">Thousands of times<\/td><\/tr> <\/tbody> <\/table> <\/div> <p>In practice, electrolytic capacitors reach hundreds of microfarads by a different trick: an oxide layer only a few hundred nanometres thick. Because d sits on the bottom of the formula, making it tiny sends C soaring \u2014 which is also why those capacitors have modest voltage ratings and fail loudly when you exceed them.<\/p> <p>The lab below lets you move all three variables at once. Change the plate area, the gap and the dielectric, and watch capacitance, stored charge and stored energy respond.<\/p>\n\n<div class=\"pf-sim-slot\"><div class=\"pf-sim-slot-header\"><span class=\"icon-dot\"><\/span><span class=\"label\">Capacitance 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\/capacitance.html?embed=1\" class=\"pf-sim-frame\" loading=\"lazy\"><\/iframe><\/div><\/div>\n\n<h2>Real-World Examples of Capacitance<\/h2> <figure style=\"margin:32px auto;max-width:640px;text-align:center;\">\n  <img decoding=\"async\" src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/07\/capacitors-paper.jpg\"\n       alt=\"Assorted capacitors showing ceramic disc, film and electrolytic types with different capacitance values\"\n       loading=\"lazy\"\n       style=\"width:100%;height:auto;border-radius:4px;\" \/ width=\"1200\" height=\"523\">\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">Ceramic, film and electrolytic capacitors. The red WIMA film capacitor is marked 0.1 microfarads at 250 V, its capacitance fixed by construction rather than by the voltage applied.<\/figcaption>\n<\/figure>\n\n<p>Capacitance shows up wherever charge needs to be stored briefly, released quickly, or sensed. Five cases give a feel for the range.<\/p> <h3>1. Camera Flash<\/h3> <p>A flash capacitor of roughly 200 \u00b5F charged to about 300 V stores around 9 J. The battery takes a second or two to fill it; the xenon tube empties it in about a millisecond, which is what makes the flash bright rather than merely warm.<\/p> <h3>2. Defibrillator<\/h3> <p>A defibrillator typically charges a capacitor of about 100 \u00b5F to roughly 2,000 V, storing 200 J. Note how strongly the voltage dominates \u2014 because U depends on V<sup>2<\/sup>, doubling the voltage quadruples the energy delivered.<\/p> <h3>3. Smoothing in a Power Supply<\/h3> <p>Rectified mains voltage arrives as a lumpy series of humps. A large capacitor across the output charges on each peak and discharges gently between them, flattening the ripple into something a circuit can actually run on.<\/p> <h3>4. Capacitive Touchscreens<\/h3> <p>Your phone screen carries a grid of tiny capacitors. A fingertip is conductive enough to alter the capacitance at one node by around a picofarad, and the controller reads that change as a touch \u2014 which is why gloves usually fail.<\/p> <h3>5. Supercapacitors<\/h3> <p>A 3,000 F supercapacitor rated at 2.7 V stores about 10.9 kJ, roughly 3 watt-hours. That is small next to a battery of the same mass, but it can be charged and discharged in seconds and survives hundreds of thousands of cycles \u2014 useful for regenerative braking and backup power.<\/p> <div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\"> <table style=\"width:100%;border-collapse:collapse;word-break:break-word;\"> <thead> <tr> <th style=\"border:1px solid #D9CFB8;padding:8px;text-align:left;\">Where you find it<\/th> <th style=\"border:1px solid #D9CFB8;padding:8px;text-align:left;\">Typical capacitance<\/th> <th style=\"border:1px solid #D9CFB8;padding:8px;text-align:left;\">In farads<\/th> <\/tr> <\/thead> <tbody> <tr><td style=\"border:1px solid #D9CFB8;padding:8px;\">DRAM memory cell<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">10\u201330 fF<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">~2 \u00d7 10<sup>-14<\/sup><\/td><\/tr> <tr><td style=\"border:1px solid #D9CFB8;padding:8px;\">Touchscreen node change from a finger<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">~1 pF<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">10<sup>-12<\/sup><\/td><\/tr> <tr><td style=\"border:1px solid #D9CFB8;padding:8px;\">Ceramic decoupling capacitor<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">100 nF<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">10<sup>-7<\/sup><\/td><\/tr> <tr><td style=\"border:1px solid #D9CFB8;padding:8px;\">Camera flash capacitor<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">~200 \u00b5F<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">2 \u00d7 10<sup>-4<\/sup><\/td><\/tr> <tr><td style=\"border:1px solid #D9CFB8;padding:8px;\">Earth, treated as an isolated sphere<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">~710 \u00b5F<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">7.1 \u00d7 10<sup>-4<\/sup><\/td><\/tr> <tr><td style=\"border:1px solid #D9CFB8;padding:8px;\">Supercapacitor<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">up to 3,000 F<\/td><td style=\"border:1px solid #D9CFB8;padding:8px;\">3 \u00d7 10<sup>3<\/sup><\/td><\/tr> <\/tbody> <\/table> <\/div> <p>That last row is worth a second look. The entire planet, treated as an isolated conducting sphere, has a capacitance comparable to a large electrolytic capacitor you could hold between two fingers \u2014 a reminder that the farad is an enormous unit.<\/p> <h2>Common Misconceptions About Capacitance<\/h2> <h3>Myth 1: A Capacitor Stores Charge<\/h3> <p>A charged capacitor has zero net charge. One plate carries +Q and the other -Q, so what the capacitor really does is separate charge and hold it apart. What it stores is <em>energy<\/em>, in the electric field between the plates.<\/p> <h3>Myth 2: A Bigger Capacitance Means More Charge<\/h3> <p>Only at the same voltage. Capacitance is charge <em>per volt<\/em>, so a 1 \u00b5F capacitor at 100 V holds ten times the charge of a 10 \u00b5F capacitor at 1 V. Always check what voltage each component is sitting at before comparing.<\/p> <h3>Myth 3: The Energy Stored Is QV<\/h3> <p>It is half that. Because voltage climbs from zero to V during charging, the average voltage each unit of charge crosses is V\/2. Writing U = QV instead of \u00bdQV is one of the most common ways to lose marks on this topic.<\/p> <h3>Myth 4: Capacitance Depends on the Voltage You Apply<\/h3> <p>It does not. C is fixed by area, separation and dielectric \u2014 the geometry of the thing. Raising the voltage raises the stored charge in exact proportion, leaving the ratio Q\/V unchanged.<\/p> <h2>How Capacitance Relates to Charge, Voltage and Current<\/h2> <p>Capacitance ties together three quantities you have already met: charge, potential difference, and the field that connects them. Each one gives a different handle on the same physics.<\/p> <p>The V in C = Q\/V is the ordinary <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/potential-difference\/\">potential difference<\/a> across the plates, and the charge separation that produces it is the same effect at work in everyday <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/static-electricity\/\">static electricity<\/a>. Between the plates sits a uniform <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/electric-field\/\">electric field<\/a> of strength E = V\/d \u2014 for a 12 V supply across a 0.1 mm gap, that is 120,000 V\/m.<\/p> <p>Charging is not instantaneous, either. Charge arrives as a current, and since <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/electric-current\/\">electric current<\/a> is the rate of charge flow, the capacitor fills at a speed set by whatever <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/electrical-resistance\/\">resistance<\/a> is in the way. The product RC is the time constant, the time to reach about 63% of the final voltage.<\/p> <h3>Capacitors in Series and Parallel<\/h3> <p>Here is a rule that catches almost everyone: capacitors combine the opposite way round to resistors.<\/p> <ul> <li><strong>In parallel<\/strong> \u2014 capacitances add: C<sub>total<\/sub> = C<sub>1<\/sub> + C<sub>2<\/sub> + \u2026 The plate areas effectively combine.<\/li> <li><strong>In series<\/strong> \u2014 reciprocals add: 1\/C<sub>total<\/sub> = 1\/C<sub>1<\/sub> + 1\/C<sub>2<\/sub> + \u2026 The total is always smaller than the smallest one.<\/li> <\/ul> <p>If that feels backwards, check it against how <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/series-parallel-circuits\/\">series and parallel circuits<\/a> behave with resistors and the symmetry becomes obvious rather than arbitrary.<\/p> <h2>Worked Problems<\/h2>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 1<\/div><div class=\"pf-problem-question\">A capacitor stores 6.0 mC of charge when connected to a 12 V supply. What is its capacitance?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n\n<strong>Solution:<\/strong>\n\nStep 1: Use the defining formula, C = Q \/ V.\n\nStep 2: Convert to SI units. Q = 6.0 mC = 6.0 \u00d7 10<sup>-3<\/sup> C, and V = 12 V.\n\nStep 3: C = (6.0 \u00d7 10<sup>-3<\/sup> C) \/ (12 V) = 5.0 \u00d7 10<sup>-4<\/sup> F.\n\n<strong>Answer: 5.0 \u00d7 10<sup>-4<\/sup> F, or 500 \u00b5F (2 s.f.)<\/strong>\n\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 2<\/div><div class=\"pf-problem-question\">How much charge sits on a 220 microfarad capacitor connected across a 9.0 V battery?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n\n<strong>Solution:<\/strong>\n\nStep 1: Rearrange C = Q \/ V to give Q = C \u00d7 V.\n\nStep 2: Substitute with units. Q = (220 \u00d7 10<sup>-6<\/sup> F) \u00d7 (9.0 V).\n\nStep 3: Q = 1.98 \u00d7 10<sup>-3<\/sup> C.\n\n<strong>Answer: 1.98 \u00d7 10<sup>-3<\/sup> C, or 1.98 mC (3 s.f.)<\/strong>\n\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 3<\/div><div class=\"pf-problem-question\">A 470 microfarad capacitor is charged to 25 V. How much energy does it store?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n\n<strong>Solution:<\/strong>\n\nStep 1: Use the energy formula U = \u00bdCV\u00b2.\n\nStep 2: Substitute with units. U = \u00bd \u00d7 (470 \u00d7 10<sup>-6<\/sup> F) \u00d7 (25 V)\u00b2.\n\nStep 3: (25)\u00b2 = 625, so U = 0.5 \u00d7 470 \u00d7 10<sup>-6<\/sup> \u00d7 625 = 0.1469 J.\n\n<strong>Answer: 0.147 J (3 s.f.)<\/strong>\n\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 4<\/div><div class=\"pf-problem-question\">Two square plates of area 0.020 square metres are separated by 0.10 mm of air. What is the capacitance?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n\n<strong>Solution:<\/strong>\n\nStep 1: Use the parallel-plate formula, C = \u03b5<sub>0<\/sub>\u03b5<sub>r<\/sub>A \/ d, with \u03b5<sub>r<\/sub> = 1.0 for air.\n\nStep 2: Convert the gap. d = 0.10 mm = 1.0 \u00d7 10<sup>-4<\/sup> m.\n\nStep 3: C = (8.854 \u00d7 10<sup>-12<\/sup> F\/m \u00d7 1.0 \u00d7 0.020 m\u00b2) \/ (1.0 \u00d7 10<sup>-4<\/sup> m) = 1.77 \u00d7 10<sup>-9<\/sup> F.\n\n<strong>Answer: 1.77 \u00d7 10<sup>-9<\/sup> F, or 1.77 nF (3 s.f.)<\/strong>\n\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 5<\/div><div class=\"pf-problem-question\">The air gap in problem 4 is filled with a dielectric of relative permittivity 4.0. What is the new capacitance, and what happens to the stored energy if the capacitor stays connected to the same supply?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n\n<strong>Solution:<\/strong>\n\nStep 1: Capacitance scales directly with \u03b5<sub>r<\/sub>, so C<sub>new<\/sub> = 4.0 \u00d7 1.77 nF = 7.08 nF.\n\nStep 2: The supply holds V constant, so use U = \u00bdCV\u00b2 with C quadrupled and V unchanged.\n\nStep 3: U is proportional to C at fixed V, so the stored energy is also 4.0 times larger. The extra energy is supplied by the battery as more charge flows onto the plates.\n\n<strong>Answer: C = 7.08 nF (3 s.f.); the stored energy increases by a factor of 4.0<\/strong>\n\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 6<\/div><div class=\"pf-problem-question\">A 3.0 microfarad and a 6.0 microfarad capacitor are connected first in series, then in parallel. Find the total capacitance in each case.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n\n<strong>Solution:<\/strong>\n\nStep 1: In series, reciprocals add: 1\/C = 1\/3.0 + 1\/6.0 = 0.3333 + 0.1667 = 0.5000 (\u00b5F)<sup>-1<\/sup>.\n\nStep 2: Invert. C<sub>series<\/sub> = 1 \/ 0.5000 = 2.0 \u00b5F, which is smaller than either capacitor.\n\nStep 3: In parallel, capacitances add directly. C<sub>parallel<\/sub> = 3.0 + 6.0 = 9.0 \u00b5F.\n\n<strong>Answer: 2.0 \u00b5F in series; 9.0 \u00b5F in parallel (2 s.f.)<\/strong>\n\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 7<\/div><div class=\"pf-problem-question\">A defibrillator charges a 100 microfarad capacitor to 2.0 kV. Find the stored energy, and the average power delivered if it discharges in 5.0 ms.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n\n<strong>Solution:<\/strong>\n\nStep 1: Energy first. U = \u00bdCV\u00b2 = \u00bd \u00d7 (100 \u00d7 10<sup>-6<\/sup> F) \u00d7 (2.0 \u00d7 10<sup>3<\/sup> V)\u00b2.\n\nStep 2: (2.0 \u00d7 10<sup>3<\/sup>)\u00b2 = 4.0 \u00d7 10<sup>6<\/sup>, so U = 0.5 \u00d7 100 \u00d7 10<sup>-6<\/sup> \u00d7 4.0 \u00d7 10<sup>6<\/sup> = 200 J.\n\nStep 3: Average power is energy divided by time. P = 200 J \/ (5.0 \u00d7 10<sup>-3<\/sup> s) = 4.0 \u00d7 10<sup>4<\/sup> W.\n\n<strong>Answer: 200 J stored; average power 4.0 \u00d7 10<sup>4<\/sup> W, or 40 kW (2 s.f.)<\/strong>\n\n<\/div><\/details><\/div>\n\n<h2>Frequently Asked Questions<\/h2>\n\n<details class=\"pf-faq-item\"><summary>What is capacitance in simple terms?<\/summary><div class=\"pf-faq-item-answer\">\n\nCapacitance is how much electric charge something stores for each volt applied across it. A capacitor with a high capacitance soaks up a lot of charge before its voltage rises much, while a low-capacitance one fills almost at once. The formula is C = Q\/V, and the unit is the farad.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the SI unit of capacitance?<\/summary><div class=\"pf-faq-item-answer\">\n\nThe SI unit of capacitance is the farad, symbol F, defined as one coulomb per volt. It is named after Michael Faraday. The farad is an inconveniently large unit, so practical components are usually rated in microfarads, nanofarads or picofarads \u2014 one microfarad is a millionth of a farad.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the formula for energy stored in a capacitor?<\/summary><div class=\"pf-faq-item-answer\">\n\nThe energy stored in a capacitor is U = \u00bdCV\u00b2, which can equally be written \u00bdQV or Q\u00b2\/(2C). Use the form that matches the quantities you already know. The factor of one half appears because the voltage rises from zero to its final value while the capacitor charges.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Why is the energy stored half QV and not QV?<\/summary><div class=\"pf-faq-item-answer\">\n\nBecause the voltage across a capacitor is not constant while it charges. The first charge to arrive crosses a nearly empty capacitor at almost no voltage, and the last crosses at the full voltage V. The average is V\/2, so the total energy comes to half of QV.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Does capacitance change with voltage?<\/summary><div class=\"pf-faq-item-answer\">\n\nNo. Capacitance is fixed by the capacitor&#8217;s physical construction \u2014 plate area, plate separation and the dielectric between the plates. Increasing the applied voltage increases the stored charge in exact proportion, so the ratio Q\/V stays the same. Real capacitors drift slightly with temperature and age, but not with applied voltage in ideal theory.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Why does adding a dielectric increase capacitance?<\/summary><div class=\"pf-faq-item-answer\">\n\nA dielectric increases capacitance because its molecules polarise in the applied field and set up an opposing field of their own. That partly cancels the field between the plates, lowering the voltage for the same stored charge. Since C = Q\/V, a smaller V for the same Q means a larger C, multiplied by the relative permittivity.\n\n<\/div><\/details>\n\n<h2>Key Takeaways<\/h2> <ul> <li>Capacitance is charge stored per volt: C = Q\/V, measured in farads (1 F = 1 C\/V).<\/li> <li>For parallel plates, C = \u03b5<sub>0<\/sub>\u03b5<sub>r<\/sub>A\/d \u2014 more area and less separation both raise C.<\/li> <li>Stored energy is U = \u00bdCV\u00b2 = \u00bdQV = Q\u00b2\/(2C), never the full QV.<\/li> <li>A charged capacitor carries no net charge; it separates charge and stores energy in the field.<\/li> <li>Capacitors add in parallel and combine reciprocally in series \u2014 the reverse of resistors.<\/li> <\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Capacitance is the charge a component stores per volt, C = Q\/V, measured in farads. This guide covers the formula, the parallel-plate equation, the energy stored in a capacitor, dielectrics, common misconceptions and seven worked problems.<\/p>\n","protected":false},"author":1,"featured_media":679,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-677","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanics"],"_links":{"self":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/677","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=677"}],"version-history":[{"count":2,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/677\/revisions"}],"predecessor-version":[{"id":683,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/677\/revisions\/683"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media\/679"}],"wp:attachment":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media?parent=677"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/categories?post=677"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/tags?post=677"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}