When a charged capacitor discharges through a resistor, the charge, current and p.d. all
Capacitors - OCR A-Level Physics
- When a charged capacitor discharges through a resistor, the chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C)., currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). and p.d. all decrease exponentiallyChanging at a rate proportional to the current value, producing a curved graph that never reaches zero..
- The rate of discharge depends on the product RC, known as the time constantThe product of resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to currentThe rate of flow of charge. Measured in amperes (A).. Measured in ohms (Ω). and capacitanceThe charge stored per unit potential difference across a capacitor. Measured in farads (F). in an RC circuit. The time taken for the charge (or voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V). Informal term for potential difference.) to fall to 1/e (about 37%) of its initial value. \tau.
- During charging, the charge and p.d. across the capacitor increase exponentially towards their maximum values, while the current decreases exponentially.
$$Q = Q_0 e^{-t/RC}$$
$$\begin{aligned}
I &= I_0 \(e^{-t/RC}\) \qquad V \\
&= V_0 \(e^{-t/RC}\)
\end{aligned}$$
- During chargingThe process of storing charge on a capacitor by connecting it to a voltage source., Q and V across the capacitor follow: $Q = Q_0(1 - e^{-t/RC}) and$ $V_C = V_0(1 - e^{-t/RC})$, while the current still decays as $I = I_0 e^{-t/RC}$.
- In both charging and discharging, the current always decays exponentially because the driving p.d. across the resistor decreases over time.