CAPACITORS
Q = CV; the energy ½CV² is the triangle under the Q–V line. And the mirror of resistors — caps in parallel ADD, in series reciprocate, with C_series × C_parallel = C₁C₂.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
Two conductors and a gap: a capacitor. Push charge onto one plate and it pulls an equal and opposite charge onto the other, held apart by the voltage between them. It is the simplest device that stores electrical energy — a bucket for charge.
The law
The charge a capacitor holds is proportional to the voltage across it: Q = CV. The constant C, the capacitance, is coulombs stored per volt applied — the slope of a straight line through the origin, the exact echo of Ohm’s law for a different quantity.
Charge & energy
The charge is one multiplication. The energy is subtler: E = ½CV². That factor of one-half is not decoration — it is the triangle beneath the Q–V line. The voltage rises as the plates fill, so the last coulomb costs more to add than the first.
Charging up
Sweep the voltage from zero and watch the plates fill, the operating point climbing the Q–V line while the energy triangle grows beneath it. Double the voltage and you quadruple the stored energy — which is why a defibrillator wants volts, not just charge.
Audit
Audited: the three energy routes ½CV², ½QV, and Q²/2C agree to the last bit; the stored energy is exactly half the QV a battery pays; and capacitors mirror resistors backwards — parallel adds, series reciprocates — with C_series × C_parallel = C₁C₂ to the bit.