A-Level Physics: Capacitor Charge and Discharge Calculations

Capacitors appear in almost every A level Physics paper, and the marks are mostly in the calculations: using the exponential equations for charge, p.d. and current, rearranging them with natural logarithms, and linking graphs of current against time and p.d. against charge to charge and energy. This year-13 material concentrates on that quantitative side; the qualitative ideas and parallel-plate capacitance are covered in the electric fields and capacitance material of this category.

The quiz (12 questions) starts with the time constant of a circuit and the percentage of the final p.d. reached after one time constant while charging. It then works through the exponential equations: the p.d. of a discharging capacitor after a given time, the current at a given time, and the time taken for the p.d. to fall to a chosen value, which needs natural logarithms (a common slip is using base-10 logarithms). Other questions find the time constant from the halving time (T½ = 0.69RC), find the total charge that flows as the area under an exponential current–time graph, and give the p.d. across a charging capacitor after a given time. Energy questions ask which expressions give the energy stored and how much energy is dissipated in the resistor when the p.d. halves, which turns out to be three-quarters of the stored energy. Two multiple-answer questions check why discharge is exponential and how the p.d. behaves during charging.

The flashcards (13 cards) give the time constant, the discharge and charging equations, the energy formulae, the halving time, the initial current, the meaning of the areas under I–t and Q–V graphs, the gradient of a ln V against t graph, the 37% and 63% values, and the units of capacitance and resistance.

The written work (8 questions) asks you to explain why discharge is exponential, carry out a full set of discharge calculations, describe the practical method for measuring a time constant with a data logger and a ln V against t graph, show that half the energy from the supply is dissipated in the resistor during charging whatever its resistance, use an I–t graph to find resistance, charge and capacitance, describe how p.d., charge and current change while charging, analyse a camera-flash circuit, and explain why the energy stored is ½QV.

The content is based on the capacitance section common to A level Physics specifications in England (for example AQA 3.7.4, capacitance, energy stored, and capacitor charge and discharge, including the related required practical).

• Use Q = Q₀e^(−t/RC), V = V₀e^(−t/RC) and I = I₀e^(−t/RC) for discharge and V = V₀(1 − e^(−t/RC)) for charging
• Calculate times from the exponential equations using natural logarithms, and use T½ = 0.69RC
• Find charge from the area under a current–time graph
• Calculate the energy stored and the energy dissipated during charging and discharging
• Describe how to measure a time constant experimentally with a ln V against t graph

Practice material written by Zestly, based on the DfE GCE AS and A level subject content for physics (DFE-00356-2014): capacitance, energy stored and capacitor charge and discharge.