CAIE A-Level Physics 19.3.2 Capacitor Time Constant τ = RC

Practise calculating and rearranging the capacitor discharge time constant tau = RC, relating it to resistance, capacitance and the decay scale.

Exam points

calculate or interpret the time constant τ = RC for a discharging capacitor
rearrange τ = RC to determine resistance or capacitance and relate the time constant to the decay scale

[Maximum number: 1]

A capacitor of capacitance $470 \mu \mathrm{~F}$ is connected to a battery of electromotive force (e.m.f.) 24 V in the circuit of Fig. 5.1.

Fig. 5.1

The two-way switch S is initially at position X.
P and Q are identical long straight wires, each with a resistance of $5.6 \mathrm{k} \Omega$ . These wires are placed near to, and parallel to, each other. Wire Q is connected to a voltmeter.

At time t=0, switch S is moved to position Y so that the capacitor discharges through wire P .

Calculate the time constant $\tau$ of the discharge circuit.

\tau=

$\tau=R C$

C1

$\begin{aligned} =5600 \times 470 \times 10^{-6} =2.6 \mathrm{~s} \end{aligned}$

A1

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19.3.2—Τ = RC for the time constant for a capacitor discharging through a resistor question 1