A-Level CAIE Physics A2 19.2 Energy stored in a capacitor Question Bank

[Maximum number: 5]

A capacitor consists of two metal plates separated by an insulator, as shown in Fig. 3.1.

Fig. 3.1

The potential difference between the plates is V. The variation with V of the magnitude of the charge Q on one plate is shown in Fig. 3.2.

Fig. 3.2

(a)

Explain why the capacitor stores energy but not charge.

[ 3 ]

(b)

Use Fig. 3.2 to determine

[ 2 ]

(i)

the loss in energy stored in the capacitor when the potential difference V is reduced from 10.0 V to 7.5 V .
energy = mJ

[ 2 ]

(a)

An isolated metal sphere has radius 45 cm .

[ 3 ]

(i)

The sphere is charged to a potential of $9.0 \times 10^{5} \mathrm{~V}$ .

A spark occurs, partially discharging the sphere so that its potential is reduced to $3.6 \times 10^{5} \mathrm{~V}$ .

Determine the energy of the spark.

[ 3 ]

(a)

A capacitor of capacitance $45 \mu \mathrm{~F}$ is connected to a variable power supply initially set at 8.0 V . The output of the power supply increases so that the potential difference (p.d.) across the capacitor increases to 9.6 V .

Calculate the increase in energy $\Delta E$ stored in the capacitor.

\Delta E=

[ 2 ]

[Maximum number: 1]

An uncharged capacitor is connected in series with a battery, a switch and a resistor, as shown in Fig. 6.1.

Fig. 6.1

The battery has e.m.f. 9.0 V and negligible internal resistance. The capacitance of the capacitor is $4700 \mu \mathrm{~F}$ .
The switch is closed at time t=0.
During the time interval t=0 to $t=4.0 \mathrm{~s}$ , the charge passing through the resistor is 22 mC .

(a)

(i)

Determine, for the capacitor at time $t=4.0 \mathrm{~s}$ ,
1. the potential difference V across the capacitor,
V= V
2. the energy stored in the capacitor.

energy =

(b)

Suggest why your answers in (a)(i) and (a)(ii) part 2 are different.

[ 1 ]

(a)

A capacitor of capacitance $12 \mu \mathrm{~F}$ is charged using a battery of e.m.f. 9.0 V , as shown in Fig. 4.2.

Fig. 4.2

Switch $S_{1}$ is closed and switch $S_{2}$ is open.

[ 4 ]

(i)

The capacitor is now disconnected from the battery by opening $\mathrm{S}_{1}$ . Calculate the energy stored in the capacitor.

energy =

[ 3 ]

(ii)

The $12 \mu \mathrm{~F}$ capacitor is now connected to an uncharged capacitor of capacitance $20 \mu \mathrm{~F}$ by closing $\mathrm{S}_{2}$ . Switch $\mathrm{S}_{1}$ remains open.
The total energy now stored in the two capacitors is $1.82 \times 10^{-4} \mathrm{~J}$ .
Suggest why this value is different from your answer in (i).

[ 1 ]

(a)

(i)

A capacitor is made of two metal plates, insulated from one another, as shown in Fig. 5.1.

Fig. 5.1

Explain why the capacitor is said to store energy but not charge.

[ 4 ]

(a)

A capacitor of capacitance $4700 \mu \mathrm{~F}$ is charged to a potential difference of 18 V . It is then partially discharged through a resistor. The potential difference is reduced to 12 V . Calculate the energy dissipated in the resistor during the discharge.
energy =
J

[ 3 ]

(a)

An isolated metal sphere is charged to a potential V. The charge on the sphere is q. The charge on the sphere may be considered to act as a point charge at the centre of the sphere.

The variation with potential V of the charge q on the sphere is shown in Fig. 5.1.

Fig. 5.1

Use Fig. 5.1 to determine

(i)

the energy required to increase the potential of the sphere from zero to 24 kV .

energy =

(a)

A second uncharged metal sphere is brought up to the sphere in (c) so that they touch. The combined capacitance of the two spheres is 18 pF .

Calculate

[ 3 ]

(i)

the change in the total energy stored on the spheres when they touch.
change = J

[ 3 ]

(a)

The variation of the potential V of an isolated metal sphere with charge Q on its surface is shown in Fig. 4.1.

Fig. 4.1

An isolated metal sphere has capacitance.

Use Fig. 4.1 to determine

(i)

the electric potential energy stored on the sphere when charged to a potential of 150 kV .

energy =

(b)

A spark reduces the potential of the sphere from 150 kV to 75 kV .

Calculate the energy lost from the sphere.
energy =
J

[ 2 ]

0 selected