Topic questions Electricity Charging & discharging capacitors
14 questions · 67 marks · about 1.5 hours
A student is using a spreadsheet to model the decay of charge on a capacitor. They are using the equation 
= – 
The student chooses a time interval of 0.5 s. At time t = 0.0 s the charge on the capacitor is 600 
C.
Part of the modelling spreadsheet is shown below.
What is the charge on the capacitor at t = 1.5 s?
A 130 
C
B 240 
C
C 246 C
D 307 C
Your answer
A group of students investigate the circuit shown in the figure below.
There are N capacitors, each of capacitance C, connected in parallel.
There are N resistors, each of resistance R, connected in series.
Initially, the students close the switch X. They then note the reading on the ammeter.
The students then open the switch. They record the time T for the reading on the ammeter to fall to half of its initial value.
The table below shows the students’ results.
| N | T | / s | ||
| 1 | 2 | 3 | Mean | |
| 1 | 14.7 | 14.1 | 14.3 | .............. |
| 2 | 50.3 | 49.6 | 50.1 | .............. |
| 3 | 126.6 | 126.3 | 125.2 | 126.0 |
| 4 | 224.4 | 224.3 | 225.9 | 224.9 |
| 5 | 356.1 | 354.3 | 345.6 | 352.0 |
| 6 | 500.4 | 512.7 | 499.5 | 504.2 |
Show that T = (ln 2)N2RC. (a)
The results table is repeated below.
Complete the last column for N = 1 and N = 2 in the table below.
| N | T | / s | ||
| 1 | 2 | 3 | Mean | |
| 1 | 14.7 | 14.1 | 14.3 | .............. |
| 2 | 50.3 | 49.6 | 50.1 | .............. |
| 3 | 126.6 | 126.3 | 125.2 | 126.0 |
| 4 | 224.4 | 224.3 | 225.9 | 224.9 |
| 5 | 356.1 | 354.3 | 345.6 | 352.0 |
| 6 | 500.4 | 512.7 | 499.5 | 504.2 |
The students begin to plot a graph of T (y-axis) against N2 (x-axis). (d)
Draw a straight line of best fit on the graph.
Calculate the gradient of the straight line of best fit.
The value of C is known to be 1000 
F ± 5%.
Use your gradient value from (iii) to find a value for R, in units of k 
, including an absolute uncertainty.
R =........ ±........ k 
Following the investigation, the students discovered that the sixth 1000 F capacitor connected to the circuit was actually two 470 
F capacitors connected in parallel.
State the type of error caused by this mistake.
Explain the effect that this error would have had on the calculated value of R.
The student decides to plot T against R to obtain a straight-line graph.
Show that the line has gradient = C ln2.
The data points plotted by the student are shown below.
1 Draw a best-fit straight line through the data points and use the gradient of this line to determine C.
2 Use your answer in (ii)1 to calculate the permittivity 
of the paper.
=........ F m–1
Define the time constant of a circuit containing a capacitor of capacitance C and a resistor of resistance R.
By drawing a suitable tangent to the graph in Fig. 6.3, calculate the maximum current in the resistor.
A student is modelling the decay of charge for a capacitor discharging through a resistor using the
Part of the modelling spreadsheet from the student is shown below.
What is the value of Q in C at t = 1.5 s?
A 700
B 720
C 729
D 800
Your answer
The diagram below shows a circuit to charge a capacitor.
The electromotive force (e.m.f.) E of the cell is 1.48 V and it has negligible internal resistance. The resistance of the resistor is 120 k
and the capacitance of the capacitor is 2000 F. At time t = 0 the capacitor is uncharged. The switch is closed at time t = 0.
Calculate the time t when the potential difference across the capacitor is 1.00 V.
A capacitor of capacitance C is connected across a strip of conductive paper.
The switch is moved from X to Y, and the time t for the potential difference across the capacitor to halve is measured.
The time t is given by the expression
t = (Ck ln2) × L
where k is the resistance of the conductive paper per unit length and L is the length of the conductive paper.
The value of C is 1.2 × 10–3 F.
In an experiment, L is changed and t measured.
The data points are plotted on a t against L grid as shown below.
Draw a straight line of best fit through the data points, and use the gradient of this line to determine k.
The diagram below shows a circuit used to charge a capacitor.
The power supply has electromotive force (e.m.f.) 10 V and negligible internal resistance. The capacitor has capacitance C and the resistor has resistance R. The switch is closed at time t = 0. The table below shows potential difference V across the resistor at various values of time t.
| V / V | 10 | 6.3 | 5.0 | 3.7 |
| t / s | 0 | 2.8 | 4.2 | 6.0 |
What is the product C × R for this circuit?
A 0 s
B 2.8 s
C 4.2 s
D 6.0 s
Your answer
A capacitor discharges through a resistor. At time t = 0 the potential difference V across the capacitor is V0. At time t = 2.0 s, V = 0.90 V0.
Which statement is not correct?
A At t = 4.0 s, V = 0.81 V0.
B The capacitor is fully discharged after t = 10 s.
C The potential difference across the resistor is the same as that for the capacitor.
D The potential difference V decreases exponentially with time t.
Your answer
A capacitor is discharged through a resistor.
The capacitor is fully charged at time t = 0. The time constant of the circuit is 10 s. The switch is closed at time t = 0. The current in the resistor is I.
Which row is correct?
| Current I at t = 0 | Current I at t = 10 s | |
| A | maximum | 0 |
| B | maximum | 37% of the current at t = 0 |
| C | 0 | 63% of the current at t = ∞ |
| D | 0 | 37% of the current at t = ∞ |
Your answer
A capacitor is charged through a resistor.
The cell has e.m.f. 1.50 V and negligible internal resistance. The capacitor is initially uncharged. The time constant of the circuit is 100 s. The switch is closed at time t = 0.
What is the potential difference across the capacitor at time t = 200 s?
A 0.20 V
B 0.55 V
C 0.95 V
D 1.30 V
Your answer
A student wishes to determine the permittivity 
of paper using a capacitor made in the laboratory.
The capacitor consists of two large parallel aluminium plates separated by a very thin sheet of paper.
The capacitor is initially charged to a potential difference V0 using a battery. The capacitor is then discharged through a fixed resistor of resistance 1.0 M
.
The potential difference V across the capacitor after a time t is recorded by a data-logger. The student uses the data to draw the ln V against t graph shown in Fig. 22.
Show that the magnitude of the gradient of the line shown in Fig. 22 is equal to
where C is the capacitance of the capacitor and R is the resistance of the resistor.
* Use Fig. 22 to determine the capacitance C of the capacitor. Describe how the student can then use this value of C to determine a value for 
. In your description, mention any additional measurements required on the capacitor.
A capacitor discharges through a resistor. At time t = 0, the charge stored by the capacitor is 600 
C. The capacitor loses 5.0 % of its charge every second.
What is the charge left on the capacitor at time t = 4.0 s?
A 111 C
B 120 C
C 480 C
D 489 C
Your answer
A capacitor of capacitance 7.2 pF consists of two parallel metal plates separated by an insulator of thickness 1.2 mm. The area of overlap between the plates is 4.0 
10−4 m2. Calculate the permittivity of the insulator between the capacitor plates.
permittivity =........ F m−1
Fig. 21 shows a circuit.
The capacitance of each capacitor is 1000 F. The resistance of the resistor is 10 k
. The cell has e.m.f. 1.5 V and negligible internal resistance.
Calculate the total capacitance C in the circuit.
C =........ F
The switch S is closed at time t = 0. There is zero potential difference across the capacitors at t = 0. Calculate the potential difference V across the resistor at time t = 12 s.
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