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CAIE A-Level Physics A2 19.2 Energy Stored in a Capacitor Questions

Practise deriving capacitor energy from the area under a Q-V graph and comparing W = 1/2 QV with equivalent capacitance formulae.

Syllabus
2028–2030
Course
Physics 9702
Level
A2

Exam points

  • determine capacitor energy from the potential–charge graph area
  • calculate and compare stored energy using W=1/2QV=1/2CV²

Covered syllabus points

19.2.1—The electric potential energy stored in a capacitor19.2.2—W = 1/2 QV = 1/2 CV 2

Question 1

[Maximum number: 3]

The variation with potential difference V of the charge Q on one of the plates of a capacitor is shown in Fig. 5.1.

Fig. 5.1

Fig. 5.1

The capacitor is connected to an 8.0 V power supply and two resistors R and S as shown in Fig. 5.2.

Fig. 5.2

Fig. 5.2

The resistance of R is 25kΩ25 \mathrm{k} \Omega and the resistance of S is 220kΩ220 \mathrm{k} \Omega.
The switch can be in either position X or position Y .

The switch is in position X so that the capacitor is fully charged.

Calculate the energy E stored in the capacitor.

E=

Question 2

[Maximum number: 7]

Question (a)

(a)

Two capacitors P and Q are connected in parallel to a power supply of voltage V. The capacitance of P is 200μ F200 \mu \mathrm{~F}. The capacitance CQC_{Q} of Q can be varied between 0 and 400μ F400 \mu \mathrm{~F}. When CQ=0C_{Q}=0, the total energy stored in the capacitors is 2.5 mJ .

[ 7 ]

Question (i)

(i)

Show that the supply voltage V is 5.0 V .

Figure for Question (i) — CAIE A-Level Physics A2
[ 2 ]

Question (ii)

(ii)

Calculate the total energy, in mJ , stored in the capacitors when CQC_{\mathrm{Q}} has its maximum value.
15
total energy = mJ

[ 3 ]

Question (iii)

(iii)

On Fig. 6.2, sketch the variation of the total energy E stored in the capacitors with CQC_{\mathrm{Q}}, as CQC_{Q} varies from 0 to 400μ F400 \mu \mathrm{~F}.

Fig. 6.2

Fig. 6.2

[ 2 ]
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