CAIE A-Level Physics A2 19.1 Capacitors and Capacitance Questions

Practise defining capacitance with C = Q/V and deriving or using equivalent capacitance for series and parallel networks.

Exam points

define capacitance and apply C=Q/V to charge, voltage and capacitance
derive and use equivalent capacitance for series and parallel networks

Covered syllabus points

19.1.1—Capacitance, as applied to both isolated spherical conductors and to 19.1.2—C = Q / V 19.1.3—C = Q / V, formulas for the combined capacitance of capacitors in series and 19.1.4—The capacitance formulas for capacitors in series and in parallel

[Maximum number: 2]

An isolated conducting sphere in a vacuum has radius r and is initially uncharged. It is then charged by friction so that it carries a final charge Q. This charge can be considered to be acting at the centre of the sphere.

By considering the electric potential at its surface, show that the capacitance C of the sphere is given by

C=4 \pi \varepsilon_{0} r

where $\varepsilon_{0}$ is the permittivity of free space.

C=Q / V
$V=Q /\left(4 \pi \varepsilon_{0} r\right)$ and so $C=Q /\left[Q /\left(4 \pi \varepsilon_{0} r\right)\right]=4 \pi \varepsilon_{0} r$

[Maximum number: 2]

A capacitor C is charged so that the potential difference (p.d.) V across its terminals is 8.0 V . The capacitor is connected into the circuit of Fig. 6.1.

Fig. 6.1

The switch is initially open. The switch is closed at time t=0.

Fig. 6.2 shows the variation of V with the charge Q on the plates of capacitor C as the capacitor discharges.

Fig. 6.2

Determine the capacitance of capacitor C . Give a unit with your answer.

C=Q / V or $E=1 / 2 C V^{2}$ $\begin{aligned} C =\left(450 \times 10^{-6}\right) / 8.0 \text { or }\left(2 \times 1.8 \times 10^{-3}\right) / 8.0^{2} =5.6 \times 10^{-5} \mathrm{~F} \end{aligned}$

[Maximum number: 5]

(a)

Three uncharged capacitors of capacitances $C_{1}, C_{2}$ and $C_{3}$ are connected in series with a battery of electromotive force (e.m.f.) E and a switch, as shown in Fig. 6.1.

Fig. 6.1

When the switch is closed, there is a charge +q on plate P of the capacitor of capacitance $C_{1}$ .
Show that the combined capacitance C of the three capacitors is given by the expression

\frac{1}{C}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} .

[ 3 ]

clear indication of equal charge on each capacitor
$E=V_{1}+V_{2}+V_{3}$ and V=Q / C
completion of algebra leading to $1 / C=1 / C_{1}+1 / C_{2}+1 / C_{3}$

(b)

A student has available four capacitors, each of capacitance $20 \mu \mathrm{~F}$ .

Draw circuit diagrams, one in each case, to show how the student may connect some or all of the capacitors to produce a combined capacitance of:

[ 2 ]

(i)

$60 \mu \mathrm{~F}$

[ 1 ]

(ii)

$15 \mu \mathrm{~F}$ .

[ 1 ]

[Maximum number: 3]

Three uncharged capacitors of capacitances $C_{1}, C_{2}$ and $C_{3}$ are connected in series with a battery of electromotive force (e.m.f.) E and a switch, as shown in Fig. 6.1.

Fig. 6.1

When the switch is closed, there is a charge +q on plate P of the capacitor of capacitance $C_{1}$ .
Show that the combined capacitance C of the three capacitors is given by the expression

\frac{1}{C}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} .

clear indication of equal charge on each capacitor
$E=V_{1}+V_{2}+V_{3}$ and V=Q / C
completion of algebra leading to $1 / C=1 / C_{1}+1 / C_{2}+1 / C_{3}$

[Maximum number: 2]

Three capacitors are connected as shown in Fig. 4.1.

Fig. 4.1

Determine the total capacitance, in $\mu \mathrm{F}$ , of the network of three capacitors.
capacitance = $\mu \mathrm{F}$

combined capacitance of parallel capacitors $=30(\mu \mathrm{~F})$ $\begin{aligned} \text { total capacitance } =(1 / 45+1 / 30)^{-1} =18 \mu \mathrm{~F} \end{aligned}$

All question bank results loaded

Covered syllabus points

Question 1

Question 2

Question 3

Question (a)

Question (b)

Question (i)

Question (ii)

Question 4

Question 5