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Capacitors - Multiple Choice

Q1. A 1μF capacitor is charged using a constant current of 10 μA for 20 s.

What is the energy finally stored by the capacitor?

E = ½ QV = ½ CV2 = ½ Q2/C

Q = It

E = ½ (It)2/C

E = ½ (10 x 10-6 x 20)2/10-6

E = 0.02 J

(Choice B)

 

A 
2 × 10-3 J
B
2 × 10-2 J
C
4 × 10-2 J
D
4 × 10-1 J

 

Q2. A capacitor of capacitance 10 μF is fully charged through a resistor R to a p.d. of 20V using the circuit shown below.

Which one of the following statements is incorrect?

A The p.d. across the capacitor is 20V.
True
B The p.d. across the resistor is 0V.
True
C The energy stored by the capacitor is 2mJ.

E = ½ Q V = ½ C V2 = ½ Q2/ C

= ½ 10 x 10-6 x 202

= 5 x 10-6 x 400

= 2 x 10-3 J - so C is true

D The total energy taken from the battery during the charging process is 2 mJ. The energy stored is 2 mJ – but energy will be dissipated as current passes through the resistor and battery – so total energy taken to store that charge will be greater than that.

Q3. A 10 mF capacitor is charged to 10V and then discharged completely through a small motor.

During this process, the motor lifts a weight of mass 0.10 kg.

If 10 % of the energy stored in the capacitor is used to lift the weight, through what approximate height will the weight be lifted?

A
0.05 m
B
0.10 m
C
0.50 m
D
1.00 m

 

E = ½ Q V = ½ C V2 = ½ Q2/ C

10% of E = 0.10 x ½ 10 x 10-3 x 102 = 0.05 J

work done = mg=Δh

0.05 = 0.10 x 9.81 x Δh

Δh = 0.05m

Choice A

Q4. A capacitor of capacitance 15 μF is fully charged and the potential difference across its plates is 8.0V. It is then connected into the circuit as shown below.

The switch S is closed at time t = 0.

Which one of the following statements is correct?

A The time constant of the circuit is 6.0 ms. time constant = RC = 400 x 103 x 15 x 10-6 = 6.0s - so this wrong!
B The initial charge on the capacitor is 12 μC. It will be 15 μF when fully charged - it will hold its full capacity - so this is wrong!
C After a time equal to twice the time constant, the charge remaining on the capacitor is Q0e2, where Q0 is the charge at time t = 0.

Q = Q0e-t/RC

if t = 2 x RC then t/RC will be 2

We will therefore get Q0e-2 not Q0e2 - so this is wrong!
D After a time equal to the time constant, the potential difference across the capacitor is 2.9V.

This ought to be correct - but we have to check!

V = V0e-t/RC

V = 8e-1

V = 2.94 volts - True

 

Q5. A capacitor of capacitance C discharges through a resistor of resistance R. Which one of the following statements is not true?

A
 The time constant will increase if R is increased. time constant = RC – so this is true
B
 The time constant will decrease if C increased. time constant = RC – so this is false
C
 After charging to the same voltage, the initial discharge current will increase if R is decreased. If you reduce the resistance current increases - so this is true.
D
 After charging to the same voltage, the initial discharge current will be unaffected if C is increased. Current and voltage are linked by the resistance not the capacitance – so this is true.

 

Q6. In the circuit shown below, the capacitor C is charged to a potential difference V when the switch S is closed.

Which line, A to D, in the table gives a correct pair of sketch graphs showing how the charge and current change with time after S is closed?

The charge will start at zero - there is no charge on the plates until you close the switch. Therefore graph 2 must show you what charge is doing.

When the switch is closed the charge build up will be rapid at first, but later charge build up will be slower because of repulsion from same charge particles. This happens in graph 2.

The rate at which charge is transferred is the current. Therefore the current graph is graph 1 - large current reducing exponentially to zero as the plates charge up to capacity.

Choice C
Charge
Current
A
graph 1
graph 1
B
graph 1
graph 2
C
graph 2
graph 1
D
graph 2
graph 2

 

Q7. The sketch graph shows how the charge stored by a capacitor varies with the potential difference across it as it is charged from a 6V battery.

Which one of the following statements is not correct?

A
 The capacitance of the capacitor is 5.0 μF.

C = Q/V

= 30μ/6 = 5 μF

- correct
B
 When the potential difference is 2V the charge stored is 10 μC. See graph - correct
C
 When the potential difference is 2V the energy stored is 10 μJ. Area under graph (equiv to ½ QV) = energy = ½(2 x 10) = 10 μJ - correct
D
 When the potential difference is 6V the energy stored is 180 μJ. Area under graph (equiv to ½ QV) = energy = ½(30 x 6) = 90 μJ - incorrect

 

Q8. A capacitor of capacitance C stores an amount of energy E when the pd across it is V. Which line, A to D, gives the correct stored energy and pd when the charge is increased by 50% ?

 
energy
p.d.
A
1.5E
1.5V
B
2.25E
1.5V
C
1.5E
2.25V
D
2.25E
2.25V

 

Q = CV

so, p.d. is proportional to Q

If charge is increased by a half then so will V - 1.5V

E = ½ QV = ½ CV2 = ½ Q2/C

E is proportional to Q2

If charge is increased by a half that is a factor of 1.5

so energy will increase by 1.52 = 2.25

Choice B


Q9. How many of the following four equations correctly represent the energy E stored by a capacitor of capacitance C when it is charged to a pd V and its charge is Q?

 

E = ½ Q2/C
E = ½ C/V2 x
E = ½ QC x
E = ½ CV2

 

E = ½ QV = ½ CV2 = ½ Q2/C

 

A
one
B
two
C
three
D
four

 

Choice B

 

Q10. A voltage sensor and a datalogger are used to record the discharge of a 10 mF capacitor in series with a 500Ω resistor from an initial pd of 6.0V. The datalogger is capable of recording 1000 readings in 10s.

Which line, A to D, in the table gives the pd and the number of readings made after a time equal to the time constant of the discharge circuit?

Time constant = CR = 10 x 10-3 x 500 = 5s

Datalogger gives 100 readings per second

Therefore in 5s it will give 500 readings.

-----------------------

V = V0e-t/RC

V = V0e-1

V = 6.0 x 0.368 = 2.2 volts

 

 
potential difference/V
number of readings
A
2.2
50
B
3.8
50
C
2.2
500
D
3.8
500

 

Choice C