(A Level) Capacitance

Learning objectives

Define capacitance for a parallel-plate capacitor and for an isolated spherical conductor, use C = Q/V, and show that an isolated sphere of radius R has C = 4πε₀R.

Derive the rules for combining capacitors in series (1/C = 1/C₁ + 1/C₂ + …) and in parallel (C = C₁ + C₂ + …) from C = Q/V, and use them for capacitor networks.

Show that the energy stored by a charged capacitor equals the area under its p.d.–charge graph, and calculate it with W = ½QV = ½CV².

Interpret the exponential fall of p.d., charge and current with time as a capacitor discharges through a resistor, including reading the time constant from a graph.

Calculate the time constant τ = RC and use x = x₀e^(−t/RC) to find the current, charge or p.d., or the time taken to reach a given value, during discharge.