V = W/q · C = Q/V · U = ½CV²
Not joules. Joules for every coulomb that goes round, which is why a torch cell and a car battery can both say 1.5 or 12 and be nothing alike. Get that one reading right and potential, capacitance and stored energy all fall into place behind it.
This page separates field, potential and potential energy, then uses them to build a capacitor and work out what it stores. By the end you'll be able to:
A capacitor is the only common component that stores energy and can give all of it back in a thousandth of a second:
Searched as: electric potential vs potential energy, what is a volt, capacitance formula, energy stored in a capacitor, parallel plate capacitor, dielectric effect.
Predict the stored energy, lock it, then change the plate area on its own and see which readouts move and which do not. 🟢 real C = ε₀εᵣA/d engine
Guess, then lock — the bench waits until you commit.
Set an area and a gap, then change the area on its own and see which of the four readouts move.
Field, potential and potential energy are three different quantities that everyday speech runs together. Six situations — name the right one.
How hard a stray charge is pushed at one particular point. Which quantity is this?
Ask whether a particular charge has been named. If it has, you are being asked about joules rather than joules per coulomb.
The two midpoint cases are the ones that separate people who know this from people who think they do.
Two hundred square centimetres of plate in air, and a target capacitance. Choose the separation — 3 attempts.
Set the gap, then measure. C = ε₀A/d.
Each claim breaks something. Tap the broken idea.
The gap is an insulator, so nothing crosses it. Charge builds on one plate and an equal amount leaves the other, which looks like current in the wires. A capacitor blocks steady current completely.
The two pushes cancel because they are vectors pointing opposite ways. Potentials are plain numbers and both are positive, so they add. At that point the field is zero and the potential is at a maximum along the line.
Energy is ½CV² and the voltage is squared. The 10 μF capacitor at 400 V stores 800 mJ while the 1000 μF one at 5 V stores 12.5 mJ — sixty-four times less, despite being a hundred times larger.
Thinking beats memorising. Sort every claim about potential and capacitance into three boxes.
A charge makes one move. Say whether the potential at its position rises, falls or does not change.
Ask whether any work would be done on a positive test charge making that move.
Closer plates hold more charge and also make a fiercer field. Every insulator has a point beyond which it simply arcs across.
C = ε₀εᵣA/d, and E = V/d rises just as fast.
Read the scene. All three are stored charge doing something you had blamed on something else.
A small battery has plenty of energy but can only release it slowly. The capacitor is charged over a few seconds and then dumps its stored energy in about a millisecond, which is a power thousands of times greater than the battery could ever supply directly.
A grid of tiny capacitors covers the screen. Your finger is a conductor at a different potential, so bringing it close changes the capacitance of the patches beneath it, and the controller works out the position from which patches changed. This is why a gloved finger often does not register.
A large smoothing capacitor charged to a few hundred volts stores a real amount of energy, and with nothing connected to drain it there is no reason for it to leave. Many designs include a bleed resistor for exactly this reason, but it is not something to rely on.
In plain terms: potential is how much energy each coulomb would carry at a place, capacitance is how many coulombs a device holds per volt, and the energy stored follows from the two.
The field tells you the push per coulomb and has a direction; the potential tells you the energy per coulomb and is just a number. That is why potential is easier to work with: you can add contributions from several charges without any geometry. Multiply it by a named charge and you get potential energy in joules, which is a third quantity again.
Apply a voltage and charge piles onto one plate while an equal amount leaves the other. How much per volt is the capacitance, and for flat plates it is ε₀εᵣA/d — bigger plates, a smaller gap and a better filling all increase it. Nothing crosses the gap at any point, which is exactly why a capacitor blocks a steady current.
Charging is work: each extra coulomb has to be pushed against the charge already there, which is where the half comes from in U = ½CV². The voltage is squared, so doubling it quadruples the energy, and a small capacitor at a high voltage routinely beats a large one at a low voltage. That is the whole design logic of a camera flash.
Every insulator has a breakdown field beyond which it conducts and arcs — about 3 MV/m for air, far more for mica — which caps how close the plates can be for a given voltage. Disconnect a charged capacitor and pulling the plates apart raises the voltage, because the charge has nowhere to go; leave it connected and the charge falls instead. And potential near a point charge goes as 1/r, not 1/r², which is a favourite place to slip.
Exams reward the method. Work it one step at a time — read the thought, predict the line, then reveal it.
Three small labs. The third one is where the square law becomes obvious.
Six wrong ideas, most of them from treating a volt as an amount rather than a rate. Tap a card to bust the myth.
Pieter van Musschenbroek charged a jar of water through a wire and received a shock he described as so violent he would not repeat it for the kingdom of France.
Franklin showed the charge sat on the glass rather than in the water, and built a flat version — two plates with an insulator between, which is still the design.
Faraday found that filling the gap with an insulating material increased the stored charge, and the unit of capacitance was later named after him.
Using porous carbon gave an effective plate area of hundreds of square metres in a small cell, finally making whole farads practical.
A memory chip holds billions of capacitors, each storing one bit and each leaking away within milliseconds unless it is refreshed.
Charged slowly by a small battery, discharged in a millisecond. The capacitor supplies a power the battery never could.
Your finger changes the capacitance of tiny patches under the glass, and the controller reads off where from which ones changed.
Keeps a clock or a memory alive for minutes after the power goes, with no battery to wear out or replace.
One sentence each: what is stored, and how fast it comes back out.
Drag the slider. Six capacitances, from a tenth of a picofarad to three thousand farads.
Sixteen orders of magnitude, and the same ratio of charge to volts underneath every one.
Each one is a build and a measurement — the measuring is what turns a demo into a project.
Build: two sheets of kitchen foil separated by paper, rolled up, with leads taped on.
Measure: the capacitance on a multimeter, then predict it from the area and thickness and compare the two.
Build: a 1000 μF capacitor, a battery, a switch and a small bulb or motor.
Measure: how long the bulb stays lit for several charging voltages, and compare with ½CV².
Build: a capacitor discharging through a large resistor, with a voltmeter across it.
Measure: the voltage every ten seconds and plot it. Find the time to fall to 37% and compare with RC.
Build: two foil plates whose overlap you can slide, with a fixed thin spacer between them.
Measure: capacitance against overlap area. It should be a straight line through the origin.
Build: the same plates and gap, filled first with air and then with a sheet of plastic or glass.
Measure: both capacitances. The ratio is the dielectric constant, and you can look it up to check.
Build: a foil pad behind card, wired to a microcontroller pin with a large resistor.
Measure: the charge time with and without a finger nearby, and calibrate it into a yes-or-no touch.
Straight answers, each one complete on its own:
Potential is the work needed per coulomb to bring charge to a point, measured in volts, and it exists at a place whether or not any charge is actually there. Potential energy is the work needed for one particular named charge, measured in joules, and it is that charge multiplied by the potential. One is a property of the place; the other needs an object.
One joule per coulomb. A 12 V battery gives 12 joules of energy to every coulomb of charge it pushes round the circuit. This is why a tiny button cell and a huge car battery can both be labelled with the same voltage: the label describes energy per coulomb, and says nothing at all about how many coulombs are available.
Yes, and the classic case is the midpoint between two equal positive charges. The two pushes are equal and opposite there, so as vectors they cancel and the field is zero, but potentials are plain numbers and both are positive, so they add to a maximum. The reverse also happens midway between a positive and an equal negative charge, where the potential is zero and the field is not.
No. The gap between the plates is an insulator and nothing crosses it. What happens is that charge piles up on one plate while an equal amount is pushed off the other, so a current flows in the wires on both sides even though nothing passes through the device. That is why a capacitor blocks a steady current completely while passing a changing one.
Because the voltage grows as you charge it. The first coulomb goes on almost for free, and each later one must be pushed against the charge already sitting there, so the work per coulomb climbs steadily from zero to the final V. The average is half of that, which gives ½QV, and substituting Q = CV turns it into ½CV².
It multiplies the capacitance by the dielectric constant of that material. The molecules line up slightly in the field and partly cancel it, so the same charge produces a smaller voltage, which means more charge per volt. Paper multiplies it by about 3.5 and water by about 80, which is why real capacitors are never simply air-filled.
It depends whether it is still connected. Left connected to the battery, the voltage is held fixed, so the falling capacitance means less charge is held and the stored energy falls. Disconnected, the charge is trapped and cannot change, so the falling capacitance forces the voltage up instead and the stored energy rises — the extra coming from the work you did pulling against the attraction.
Because it is defined as one coulomb held per volt, and a coulomb is an enormous amount of charge. Two flat plates of 200 square centimetres a millimetre apart give under two hundred picofarads, which is less than a billionth of a farad. Only with the huge effective areas of porous carbon do whole farads become practical, which is why supercapacitors are quoted in them.
Spot these before the exam does.
Seven question formats, the way LLOS.ai serves them — multiple choice, multiple-correct, fill-in-the-blank, match, sequence, read-think-connect, and write-your-own. Every question has layered hints: a quick nudge, the reasoning, then a deeper connection — so a wrong answer opens a door, never a dead end. 🟢 received from a board-tagged question bank · seed toward 2,000
Pick your board — the set re-tunes to its wording and emphasis. Competitive draws the JEE / NEET / Olympiad lane.
Four capacitors, four different voltages. Tap them in order, most energy stored first. Then read the arithmetic — and see what the square does.
A thousand microfarads, charged to five volts from a small battery.
Ten microfarads, charged to four hundred volts from a mains supply.
A hundred microfarads, charged to fifty volts.
One microfarad, charged to a thousand volts.
Tap the four in the order you believe, most energy stored first.
Read the 12 on a battery as joules per coulomb and almost everything else in electricity stops being a set of formulas to memorise.