Key Equations

Capacitors - OCR A-Level Physics

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Capacitance
$$C = \frac{Q}{V}$$
  • Where:
    • $C$ = F
    • $Q$ = C
    • $V$ = V
Definition of capacitance. Use when relating charge stored to p.d.
Energy stored (charge-voltage form)
$$E = \frac{1}{2}QV$$
  • Where:
    • $E$ = J
    • $Q$ = C
    • $V$ = V
Area under the Q-V graph. Primary energy formula.
Energy stored (capacitance-voltage form)
$$E = \frac{1}{2}CV^2$$
  • Where:
    • $E$ = J
    • $C$ = F
    • $V$ = V
Substitute Q = CV into E = \frac{1}{2}QV. Most commonly used form.
Energy stored (charge-capacitance form)
$$E = \frac{Q^2}{2C}$$
  • Where:
    • $E$ = J
    • $Q$ = C
    • $C$ = F
Substitute V = Q/C into E = \frac{1}{2}QV. Use when voltage is not given. Must be memorised.
Parallel plate capacitance
$$C = \frac{\epsilon_0 \epsilon_r A}{d}$$
  • Where:
    • $C$ = F
    • $\epsilon_0$ = F \(m^{-1}\)
    • $A$ = \(m^{2}\)
    • $d$ = m
For a parallel plate capacitor with dielectric. Without dielectric, \epsilon_r = 1.
Exponential discharge (charge)
$$Q = Q_0 e^{-t/RC}$$
  • Where:
    • $Q$ = C
    • $t$ = s
    • $R$ = \Omega
    • $C$ = F
Charge remaining on a discharging capacitor at time t.
Time constant
$$\tau = RC$$
  • Where:
    • $\tau$ = s
    • $R$ = \Omega
    • $C$ = F
Time for Q to fall to 37% of initial value. After 5\tau the capacitor is effectively discharged.
Capacitors in series
$$\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2}$$
  • Where:
    • $C$ = F
Total capacitance is always less than the smallest individual capacitance. Opposite rule to resistors. Must be memorised.
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