Higher
-o-O-oCapacitors
-o-O-oPast Paper
questions
1991 - 2001
1995 Q35
A resistor and capacitor are connected in series with an a.c. supply of voltage Vs as shown below.
A voltage Vc is produced across the capacitor.
The frequency of the supply can be changed.
When the frequency of the supply is 100 Hz, the ratio Vc/Vs equals 0.5.
The frequency of the supply voltage Vs is now increased to 1000 Hz while its amplitude is kept
constant.
State whether the ratio Vc/ Vs will increase, decrease or be unchanged.
Justify your answer.
1993 Q5 (part)
(b) The circuit below shows a capacitor connected to a lamp and a signal generator.
When the frequency of the signal generator is set at 100 Hz, the lamp glows.
The frequency of the signal generator is now altered while the amplitude is kept constant.
The lamp glows more brightly.
Explain this effect.
1991 Q6
The diagram shows the flash-lamp circuit for a camera.
Initially the capacitor is uncharged and switches S and P are open. Switch S is now closed.
(a) Sketch a graph showing how the current in resistor R varies with time from the instant when S is
closed until the capacitor is fully charged.
(b) Calculate the energy stored in the capacitor when it is fully charged.
(c) When the camera shutter is operated, switch S is opened and switch P is closed.
The capacitor now fully discharges through the flash-lamp in a time of 1.6 ms.
What is the average power developed in the flash-lamp?
(d) The following information is marked on the capacitor: 47µF, 300 V.
This means that the maximum voltage that should be applied across the capacitor is 300 V.
Could this capacitor be safely connected to a 240 V a.c. supply?
Justify your answer.
1992 Q6
The following circuit is set up to investigate the charging of a capacitor.
At the start of the experiment the capacitor is uncharged.
(a) The graph below shows how the p.d. Vc across the capacitor varies with time from the instant
the switch S is closed.
Sketch a graph showing how the p.d. VR across the resistor varies with time during the first 10 s
of charging.
(b) Calculate the current in the circuit at the instant the p.d. across the capacitor is 6.0 V.
(c) (i) When the capacitor is fully charged, it is removed from the circuit and connected across
a 10 Ω resistor.
What is the total energy dissipated in the resistor?
(ii) In another experiment, the fully charged capacitor is connected across a 20 Ω resistor
instead of the 10 Ω resistor.
How does the energy dissipated in this resistor compare with that calculated in part (i)?
You must justify your answer.
1994 Q8
The circuit shown below is used to investigate the charging and discharging of a capacitor.
The capacitor is repeatedly charged and discharged by switching S between contacts 1 and 2.
(a) For one setting of R1 and R2 the following trace is obtained on the oscilloscope.
The time base of the oscilloscope is set at 5 ms per centimetre and the Y gain is set at 2 V per
centimetre.
Calculate the frequency of the vibrating switch.
(b) With the settings of the oscilloscope unaltered, a new trace is produced when the resistance of
one of the variable resistors is changed.
(i) State which one of the variable resistors was changed and whether its resistance was
increased or decreased. justify your answer.
(ii) Calculate the charge lost by the capacitor each time the switch is in the discharge position.
1996 Q7
A student is investigating the charging and discharging of a 10 000 µF capacitor using the circuit
shown below. The 6 V supply has negligible internal resistance.
Initially the capacitor is uncharged and the switch is in position Y. The switch is moved to position X
until the capacitor is fully charged and then finally back to position Y. The graphs below show the p.d.
Vc across the capacitor and the current Ic in the ammeter during this process.
(a) (i) State the value of the p.d. across the capacitor when it is fully charged.
(ii) Calculate the maximum current during the charging process.
(iii) Sketch a graph showing how the p.d. across resistor R varies with time during the charging
process. Numerical values are not required.
(b) The student deduces from the graph of current against time for the discharge that the resistance of
the lamp is less than 800 Ω.
Explain why the student's deduction is correct.
(c) Calculate the energy stored in the capacitor when it is fully charged.
1997 Q7
(a) A capacitor of capacitance 220 µF is connected in series with a 150 kΩ resistor, a switch and
an ammeter. A d.c. power supply of negligible internal resistance is connected to the circuit as
shown below.
A stopclock is started and after 10 seconds the switch S is closed. Ammeter readings are noted at
regular intervals until a time of 80 s is shown on the stopclock.
The graph below shows how the current in the circuit varies with time.
(i) Calculate the voltage V of the d.c. power supply.
(ii) At what time on the stopclock does the p.d. across the resistor equal 6 V?
(iii) What is the p.d. across the capacitor when the p.d. across the resistor is 6 V?
(b) A magazine article on the resuscitation of a heart attack victim describes the equipment used.
This equipment uses a 16 µF capacitor which is charged until the p.d. across it is 6 kV.
The capacitor is then fully discharged to give the heart a shock.
The discharge time is 2 ms.
(i) When the capacitor is fully charged, calculate:
(A) the charge stored;
(B) the energy stored.
(ii) Calculate the average current during discharge.
1998 Q6
(a) A capacitor has a value of 5µF.
Explain in terms of electric charge what this means.
(b) The 5µF capacitor shown in the circuit below is initially uncharged.
The circuit is connected to a computer and switch S is closed.
The monitor of the computer displays a graph of current against time as the capacitor charges.
The battery has negligible internal resistance.
(i) Calculate the resistance of R1
(ii) The resistor R1 is replaced by another resistor R2.
The resistance of R2 is half that of R1.
The capacitor is discharged and the experiment repeated.
Sketch the graph of charging current against time when R2 is used. Include values on the axes.
(c) In the following circuit a variable resistor R is used to keep the current constant as a different
capacitor charges. The graphs on the monitor show how the charging current and p.d. across the
capacitor vary with time after switch S is closed.
(i) What adjustment must be made to the variable resistor R so that a constant charging current
is produced?
(ii) Show by calculation that 10 seconds after switch S is closed, the charge on the capacitor
is 1 mC.
(iii) Calculate the capacitance of C.
1999 Q7
A capacitor is connected across a variable frequency supply as shown in the circuit below.
The output of the supply has constant amplitude.
(a) (i) At a certain frequency, the current in the circuit is 200 mA r.m.s.
Calculate the value of the peak current in the circuit.
(ii) The frequency of the output from the supply is now slowly increased.
Sketch the graph of current against frequency for this circuit.
Numerical values are not required but the axes should be clearly labelled.
(b) An uncharged capacitor and a resistor are connected across a 12 V d.c. supply with negligible
internal resistance as shown below.
(i) The switch, S, is now closed and the capacitor charges.
What charge is stored on the capacitor when the reading on the ammeter is 2 mA?
(ii) The capacitor is allowed to become fully charged.
Calculate the energy now stored in the capacitor.
2000 Q7
A 15 µF capacitor is connected to a 4.5 V battery, a 200 kΩ resistor and a switch as shown in the
diagram below. The battery, has negligible internal resistance.
The capacitor is initially uncharged. Switch S is now closed.
The graph below shows how the voltage across the capacitor increases with time after switch S is
closed.
(a) (i) What is the voltage across the resistor immediately after switch S is closed?
(ii) Sketch a graph showing how the current in the circuit varies with time after switch S is
closed. Numerical values on the axes are not required.
(iii) Calculate the current in the resistor 8 seconds after switch S is closed.
(b) (i) Explain why work must be done to charge the capacitor.
(ii) Calculate the energy stored in the capacitor when it is fully charged.
2001 Q7
A toy car contains an electric circuit with a 10 000 µF capacitor and an electric motor.
A supply unit is
used to provide the energy that is stored in the capacitor.
(a) A circuit diagram of the supply unit and capacitor-motor circuit is shown below.
The capacitor is initially uncharged. It is then charged from the supply unit of e.m.f. 3.0 V.
Switch S2 is open during the charging process.
(i) Sketch a graph to show how the p.d. across the capacitor varies with time during the
charging of the capacitor, from the instant switch S is closed.
Your graph must show values for the initial p.d. and the final p.d. across the capacitor.
(ii) Calculate the energy stored in the capacitor when it is fully charged.
(b) When the capacitor is fully charged, the car is removed from the supply unit.
Switch S2 is now closed.
The motor operates as the capacitor discharges.
The car has a mass of 5.0x10-2 kg.
(i) Calculate the maximum speed that could be achieved by the car.
(ii) Give one alteration that could be made to the circuit to increase the maximum speed that
could be achieved by the car.
1992 Q36.
A student sets up the circuit shown below.
When the frequency of the supply is set at 1 kHz, the trace on the oscilloscope is as shown below.
The frequency is now increased to 2 kHz while the oscilloscope controls are left unaltered.
Make a sketch, with grid lines as shown, of the trace you would now expect to see on the oscilloscope.