Capacitors & Capacitance — Structured Questions (Cambridge International A-Level Physics): Exam Questions

Two capacitors, X and Y, of capacitance 25 μF and 88.5 μF respectively, are connected in parallel to a battery of emf 6.0 V, as shown in Fig. 1.1

Fig. 1.1

The plates of both capacitor X and capacitor Y are separated by a vacuum.

Complete Table 1.1 for this circuit.

Table 1.1

Extract:

Two capacitors, X and Y, of capacitance 25 μF and 88.5 μF respectively, are connected in parallel to a battery of emf 6.0 V, as shown in Fig. 1.1. Fig. 1.1. The plates of both capacitor X and capacitor Y are separated by a vacuum. Capacitor X: capacitance 25.0 μF; Capacitor Y: capacitance 88.5 μF.

The total capacitance $C_{total}$ for two capacitors $C_{1}$ and $C_{2}$ connected in parallel is given by the equation:

$C_{total}=C_{1}+C_{2}$

Using the equation given, calculate the total capacitance of the circuit shown in Fig. 1.1 in Farads, F.

Extract:

Two capacitors, X and Y, of capacitance 25 μF and 88.5 μF respectively, are connected in parallel to a battery of emf 6.0 V, as shown in Fig. 1.1. The plates of both capacitor X and capacitor Y are separated by a vacuum.

A dielectric material is inserted into the space between the plates of capacitor Y in Fig. 1.1.

State how the capacitance of capacitor Y changes with an added dielectric material.

The graph in Fig. 1.2 represents the equation Q = CV.

Fig. 1.2

State the quantities represented by each axis.

State the relationship between the capacitance of a capacitor and the charge stored.

A parallel plate capacitor X of capacitance 300 μF is fully charged to a potential difference of 8 V.

Calculate the charge stored by X when it is fully charged.

Extract:

A parallel plate capacitor X of capacitance 300 μF is fully charged to a potential difference of 8 V.

A graph showing how the charge stored Q by capacitor X varies with the potential difference V across it is shown in Fig. 1.1.

Fig. 1.1

State the value of the gradient of the line shown in Fig. 1.1.

Give a reason for your answer.

Extract:

A parallel plate capacitor X of capacitance 300 μF is fully charged to a potential difference of 8 V.

A parallel plate capacitor Y is placed in series with the parallel plate capacitor X. Capacitor Y has a capacitance of 200 µF.

Calculate the combined capacitance of capacitors X and Y in this arrangement.

Define the capacitance of a parallel plate capacitor.

Two capacitors, of capacitances, C_A and C_B, are connected in parallel to a power supply of electromotive force (e.m.f.) E, as shown in Fig. 1.1.

Fig. 1.1

Determine an expression for the combined capacitance C_C of the two capacitors.

Two capacitors of capacitances 18 μF and 51 μF, and resistor of resistance 4.5 kΩ, are connected into the circuit of Fig. 1.2.

Fig. 1.2

The battery has an e.m.f of 8 V.

(i) Calculate the combined capacitance of the two capacitors.

(ii) The two-way switch S is initially at position P, so that the capacitors are fully charged.

Use the information in (c) (i) to calculate the total energy stored in the two capacitors.

total energy = .................................. J [2]

Three capacitors, each of capacitance 27 μF, are connected as shown in Fig. 1.1.

Fig. 1.1

Calculate the total capacitance between points P and Q.

capacitance = ..................................... μF

Extract:

Three capacitors, each of capacitance 27 μF, are connected as shown in Fig. 1.1. [Fig 1.1: one 27 μF capacitor in series with a parallel combination of two 27 μF capacitors, between points P and Q]. From part (a): Capacitance of each capacitor, C = 27 × 10^−6 F; Capacitance across the parallel combination, C_P = 54 × 10^−6 F; total series capacitance = 18 μF.

The maximum safe potential difference that can be applied across any one capacitor is 4 V.

Determine the maximum safe potential difference that can be applied between points P and Q.

potential difference = ...................................... V

A capacitor consists of an insulator separating two metal plates, as shown in Fig. 1.3.

Fig. 1.3

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. 1.4.

Fig 1.4

Explain why the capacitor stores energy but not charge.

Extract:

A capacitor consists of an insulator separating two metal plates, as shown in Fig. 1.3. 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. 1.4.

Use Fig. 1.4 to determine:

(i) the capacitance of the capacitor

capacitance = ................................. μF [2]

(ii) the loss in energy stored in the capacitor when the potential difference *V *is reduced from 8 V to 6 V.

energy = ................................. mJ [2]

State two functions of capacitors connected in electrical circuits.

Three capacitors are connected in parallel to a power supply as shown in Fig. 1.1.

Fig. 1.1

The capacitors have a capacitance C_A, C_B and C_C. The power supply provides a potential difference E.

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

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

$C_{T}=C_{A}+C_{B}+C_{C}$

A student has available three capacitors, each of capacitance 24 μF.

Draw circuit diagrams, one in each case, to show how the student connects the three capacitors to provide a combined capacitance of:

(i) 36 μF

(ii) 16 μF