Physics / A2 level
Describe charge storage and the energy transferred while charging.
A capacitor stores separated charge on conductors. Capacitance is charge magnitude on one conductor divided by their potential difference; it depends on geometry and the dielectric.
Charging transfers energy to the electric field. During discharge through a fixed resistor, charge, current and voltage decay exponentially in the ideal model. The time constant RC is a time scale, not the time for a mathematically complete discharge.
Capacitance C = Q/V relates the charge magnitude on one plate to the potential difference between plates. The two plates of a typical initially neutral capacitor carry opposite charges; adding their signed charges does not give the Q used in this equation. Capacitance depends on geometry and dielectric properties. Increasing a source voltage changes stored charge without necessarily changing the capacitance of an ideal component.
Parallel capacitors share voltage and their charges add, so equivalent capacitances add. Series capacitors in a simple initially uncharged chain have equal charge magnitude, while their potential differences add; reciprocals of capacitance therefore add. Two identical 10 μF capacitors give 20 μF in parallel but 5 μF in series. Identify the connections before choosing a rule remembered from resistor networks.
As charge builds, further charge separation requires increasing work against the electric field. Stored energy is ½QV = ½CV² = Q²/(2C). Doubling voltage at fixed capacitance quadruples stored energy. In the simple circuit charging an initially uncharged capacitor from a constant-voltage source through a resistor, the source transfers CV² and half remains stored; the other half is dissipated in the idealised resistive charging process.
For an ideal discharge through a fixed resistor, Q = Q₀e^(−t/RC); voltage and current magnitude also decay exponentially. After one time constant RC, about 37% of the original charge remains, not zero. Larger resistance or capacitance prolongs the discharge. A straight logarithmic charge–time graph can reveal the time constant, but real leakage, meter loading and component tolerances can change measured behaviour.
Exponential decay removes a fixed fraction over each equal time interval. One time constant leaves e⁻¹ of the initial charge; it does not remove a fixed total amount.
Capacitance in farads.
Stored energy.
Ideal discharge through resistance R.
A 2.0 μF capacitor is charged to 10 V. How much energy is stored?
E = ½ × 2.0 × 10⁻⁶ × 10² = 1.0 × 10⁻⁴ J = 100 μJ.
Compare simulated capacitors at two voltages. Do not handle high-voltage capacitors, which may remain charged.
Use plate geometry for capacitance and circuits for charging or discharge where the component controls permit. These models do not justify handling real high-voltage capacitors, which may retain dangerous energy.
The capacitances add.
Parallel capacitors share voltage and their charges add.
100 μJ
E = ½ × 2.0 × 10⁻⁶ × 10² = 1.0 × 10⁻⁴ J = 100 μJ.
0.37
Q/Q₀ = e⁻¹ ≈ 0.37.