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A-Level CAIE Physics 19 1 Capacitors And Capacitance Question Bank

Practice A-Level CAIE Physics 19 1 Capacitors And Capacitance questions by syllabus topic with past-paper context, marks, difficulty and question previews on Eduninja.

10 matching questions · Open interactive library

Question 3

3

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

structured8 marks

Question 3(a)

3(a)

Explain why the capacitor stores energy but not charge.

Mediumstructured3 marks

Answer

charges on plates are equal and opposite so no resultant charge energy stored because there is charge separation

Question 3(b)

3(b)

Use Fig. 3.2 to determine

structured2 marks

Question 3(b)(i)

3(b)(i)

the capacitance of the capacitor, capacitance = \(\mu \mathrm{F}\)

Easystructured2 marks

Answer

capacitance =Q / V

Question 3(c)

3(c)

Three capacitors X, Y and Z , each of capacitance \(10 \mu \mathrm{~F}\), are connected as shown in Fig. 3.3. Initially, the capacitors are uncharged. A potential difference of 12 V is applied between points A and B . Determine the magnitude of the charge on one plate of capacitor X. charge = \(\mu \mathrm{C}\)

Mediumstructured3 marks

Answer

combined capacitance of \(\mathrm{Y} \& \mathrm{Z}=20 \mu \mathrm{~F}\) or total capacitance \(=6.67 \mu \mathrm{~F} \quad\) C1 p.d. across capacitor \(\mathrm{X}=8 \mathrm{~V}\) or p.d. across combination \(=12 \mathrm{~V}\) C1 charge \(=10 \times 10^{-6} \times 8\) or \(6.67 \times 10^{-6} \times 12\)

Question 4

4

2 marks

Question 4(a)

4(a)

An insulated metal sphere of radius R is situated in a vacuum. The charge q on the sphere may be considered to be a point charge at the centre of the sphere.

structured2 marks

Question 4(a)(i)

4(a)(i)

State a formula, in terms of R and q, for the potential V on the surface of the sphere.

Easystructured1 marks

Answer

\(V=q / 4 \pi \varepsilon_{0} R\)

Question 4(a)(ii)

4(a)(ii)

Define capacitance and hence show that the capacitance C of the sphere is given by the expression

Mediumstructured1 marks

Answer

(capacitance is) ratio of charge and potential or \(q / V C=q / V=4 \pi \varepsilon_{0} R\)

Question 4(b)

4(b)

An isolated metal sphere has radius 45 cm .

structured0 marks

Question 4(b)(i)

4(b)(i)

Use the expression in (a)(ii) to calculate the capacitance, in picofarad, of the sphere.

Easystructured0 marks

Question 5

5

4 marks

Question 5(b)

5(b)

An isolated metal sphere is to be used to store charge at high potential. The charge stored may be assumed to be a point charge at the centre of the sphere. The sphere has a radius of 25 cm . Electrical breakdown (a spark) occurs in the air surrounding the sphere when the electric field strength at the surface of the sphere exceeds \(1.8 \times 10^{4} \mathrm{Vcm}^{-1}\).

structured4 marks

Question 5(b)(i)

5(b)(i)

Show that the maximum charge that can be stored on the sphere is \(12.5 \mu \mathrm{C}\).

Mediumstructured2 marks

Answer

\(E=Q / 4 \pi \varepsilon_{0} r^{2} \quad\) C1 \(Q=1.8 \times 10^{4} \times 10^{2} \times 4 \pi \times 8.85 \times 10^{-12} \times\left(25 \times 10^{-2}\right)^{2} \quad\) M1 \(Q=1.25 \times 10^{-5} \mathrm{C}=12.5 \mu \mathrm{C} \quad \mathrm{AO}\)

Question 5(b)(ii)

5(b)(ii)

Calculate the potential of the sphere for this maximum charge. potential = V

Mediumstructured2 marks

Answer

\(V=Q / 4 \pi \varepsilon_{0} r\) (Do not allow use of V= Er unless explained)

Question 4

4

2 marks

Question 4(a)

4(a)

Three capacitors are connected as shown in Fig. 4.1. Determine the total capacitance, in \(\mu \mathrm{F}\), of the network of three capacitors. capacitance = \(\mu \mathrm{F}\)

Mediumstructured2 marks

Answer

combined capacitance of parallel capacitors \(=30(\mu \mathrm{~F})\) C1 \[ \begin{aligned} \text { total capacitance } =(1 / 45+1 / 30)^{-1} =18 \mu \mathrm{~F} \end{aligned} \] A1

Question 4

4

7 marks

Question 4(a)

4(a)

State two functions of capacitors connected in electrical circuits. 1. 2.

Easystructured2 marks

Answer

e.g. store energy (do not allow 'store charge') in smoothing circuits blocking d.c. in oscillators any sensible suggestions, one each, max. 2

Question 4(b)

4(b)

Three capacitors are connected in parallel to a power supply as shown in Fig. 4.1. The capacitors have capacitances \(C_{1}, C_{2}\) and \(C_{3}\). The power supply provides a potential difference V.

structured3 marks

Question 4(b)(i)

4(b)(i)

Explain why the charge on the positive plate of each capacitor is different.

Mediumstructured1 marks

Answer

potential across each capacitor is the same and Q=C V

Question 4(b)(ii)

4(b)(ii)

Use your answer in (i) to show that the combined capacitance C of the three capacitors is given by the expression

Mediumstructured2 marks

Answer

total charge \(Q=Q_{1}+Q_{2}+Q_{3}\) \(C V=C_{1} V+C_{2} V+C_{3} V\) (allow Q=C V here or in (i)) so \(C=C_{1}+C_{2}+C_{3}\)

Question 4(c)

4(c)

A student has available three capacitors, each of capacitance \(12 \mu \mathrm{~F}\). Draw circuit diagrams, one in each case, to show how the student connects the three capacitors to provide a combined capacitance of

structured2 marks

Question 4(c)(i)

4(c)(i)

\(8 \mu \mathrm{~F}\),

Easystructured1 marks

Question 4(c)(ii)

4(c)(ii)

\(18 \mu \mathrm{~F}\).

Easystructured1 marks

Question 4

4

6 marks

Question 4(a)

4(a)

State two functions of capacitors in electrical circuits. 1. 2.

Easystructured2 marks

Answer

e.g. storing energy separating charge blocking d.c. producing electrical oscillations tuning circuits smoothing preventing sparks timing circuits (any two sensible suggestions, 1 each, max 2)

Question 4(b)

4(b)

Three uncharged capacitors of capacitance \(C_{1}, C_{2}\) and \(C_{3}\) are connected in series, as shown in Fig. 4.1. A charge of +Q is put on plate A of the capacitor of capacitance \(C_{1}\).

structured4 marks

Question 4(b)(i)

4(b)(i)

State and explain the charges that will be observed on the other plates of the capacitors. You may draw on Fig. 4.1 if you wish.

Mediumstructured2 marks

Answer

-Q (induced) on opposite plate of \(\mathrm{C}_{1}\) by charge conservation, charges are -Q,+Q,-Q,+Q,-Q

Question 4(b)(ii)

4(b)(ii)

Use your answer in (i) to derive an expression for the combined capacitance of the capacitors.

Mediumstructured2 marks

Answer

total p.d. \(V=V_{1}+V_{2}+V_{3}\) \(Q / C=Q / C_{1}+Q / C_{2}+Q / C_{3}\) \(1 / C=1 / C_{1}+1 / C_{2}+1 / C_{3}\)

Question 5

5

A charged metal sphere is isolated in space. Measurements of the electric potential V are made for different distances x from the centre of the sphere. The variation with distance x of the potential V is shown in Fig. 5.1.

structured2 marks

Question 5(b)

5(b)

The charge on the sphere is \(8.0 \times 10^{-9} \mathrm{C}\).

structured2 marks

Question 5(b)(ii)

5(b)(ii)

The sphere acts as a capacitor. Determine the capacitance of the sphere. capacitance = F

Mediumstructured2 marks

Answer

\[ \begin{aligned} \text { capacitance } =Q / V =\left(8.0 \times 10^{-9}\right) /\left(3.6 \times 10^{3}\right) =2.2 \times 10^{-12} \mathrm{~F} \end{aligned} \] A1

Question 5

5

6 marks

Question 5(a)

5(a)

1 marks

Question 5(a)(i)

5(a)(i)

Define capacitance.

Easystructured1 marks

Answer

ratio of charge and potential (difference)/voltage (ratio must be clear) B1

Question 5(b)

5(b)

Three uncharged capacitors X, Y and Z , each of capacitance \(12 \mu \mathrm{~F}\), are connected as shown in Fig. 5.2. A potential difference of 9.0 V is applied between points A and B .

structured5 marks

Question 5(b)(i)

5(b)(i)

Calculate the combined capacitance of the capacitors X, Y and Z . capacitance = \(\mu \mathrm{F}\)

Mediumstructured2 marks

Answer

capacitance of Y and Z together is \(24 \mu \mathrm{~F} \quad \mathrm{C} 1\) 1 / C=1 / 24+1 / 12 \(C=8.0 \mu \mathrm{~F}\) (allow 1 s.f.) A1

Question 5(b)(ii)

5(b)(ii)

Explain why, when the potential difference of 9.0 V is applied, the charge on one plate of capacitor X is \(72 \mu \mathrm{C}\).

Mediumstructured2 marks

Answer

some discussion as to why all charge of one sign on one plate of X B1 \(Q=(C V=) 8.0 \times 10^{-6} \times 9.0 \quad\) M1 \(=72 \mu \mathrm{C}\) A0

Question 5(b)(iii)

5(b)(iii)

Determine 1. the potential difference across capacitor X , potential difference = V 2. the charge on one plate of capacitor Y . charge = \(\mu \mathrm{C}\)

Hardstructured1 marks

Answer

1. \(\quad V=\left(72 \times 10^{-6}\right) /\left(12 \times 10^{-6}\right)\) \(=6.0 \mathrm{~V}\) (allow 1 s.f.) (allow 72/12) A1 2. either \(Q=12 \times 10^{-6} \times 3.0\) or charge is shared between Y and \(Z \quad\) C1 charge \(=36 \mu \mathrm{C}\) A1 Must have correct voltage in (iii)1 if just quote of \(36 \mu C\) in (iii)2.

Question 5

5

6 marks

Question 5(a)

5(a)

State two functions of capacitors in electrical circuits. 1. 2.

Easystructured2 marks

Answer

e.g. 'storage of charge' / storage of energy blocking of direct current producing of electrical oscillations smoothing (any two, 1 mark each)

Question 5(b)

5(b)

Three capacitors, each marked ' \(30 \mu \mathrm{~F}, 6 \mathrm{~V}\) max', are arranged as shown in Fig. 5.1. Determine, for the arrangement shown in Fig. 5.1,

structured4 marks

Question 5(b)(i)

5(b)(i)

the total capacitance, capacitance = \(\mu \mathrm{F}\)

Mediumstructured2 marks

Answer

capacitance of parallel combination \(=60 \mu \mathrm{~F} \quad \mathrm{C} 1\) total capacitance \(=20 \mu \mathrm{~F} \quad\) A1

Question 5(b)(ii)

5(b)(ii)

the maximum potential difference that can safely be applied between points A and B. potential difference = V

Mediumstructured2 marks

Answer

p.d. across parallel combination \(=\frac{1}{2} \times\) p.d. across single capacitor C1 maximum is 9 V A1

Question 4

4

1 marks

Question 4(a)

4(a)

Define capacitance.

Easystructured0 marks

Answer

charge / potential (difference) (ratio must be clear) B1 [1]

Question 4(b)

4(b)

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

structured1 marks

Question 4(b)(ii)

4(b)(ii)

This isolated sphere has capacitance. Use your answers in (a) and (b)(i) to show that the capacitance of the sphere is proportional to its radius.

Mediumstructured1 marks

Answer

\(C=Q / V=4 \pi \varepsilon_{0} r\) and \(\underline{4 \pi \varepsilon_{0}} \underline{\text { is constant }} \quad\) M1 so \(C \propto r\) A0