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5 (a) Define electric potential difference (p.d.).
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(b) A power supply, three resistors and a component X are connected in the circuit shown
in Fig. 5.1.
230 V
7.0 A + –
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0.86 Ω
I1 2.4 Ω X
I2 170 Ω
Fig. 5.1
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The power supply has an electromotive force (e.m.f.) of 230 V and negligible internal
resistance. The current in the power supply is 7.0 A.
(i) Identify component X.
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(ii) Show that the p.d. across the resistor of resistance 0.86 Ω is 6.0 V.
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[1]
(iii) Determine the current I1.
I1 = ....................................................... A [2]
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(iv) Calculate the p.d. across component X.
p.d. = ...................................................... V [2]
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(v) Calculate the power dissipated in component X.
power = ..................................................... W [2]
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(vi) The purpose of the circuit is to provide power to component X.
Determine the percentage efficiency of the circuit.
efficiency = ......................................................% [2]
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(vii) The resistor of resistance 170 Ω is removed, leaving an open circuit in the lower branch
of the circuit. There is no change to the resistance of component X.
State whether the current in the power supply increases, decreases or remains the same.
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[Total: 12]
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6 (a) Define resistance.
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(b) A cylindrical metal wire of length 2.4 m and cross-sectional area 8.0 × 10–6 m2 has a resistance
of 0.33 Ω. There is a current in the wire of 4.7 A.
(i) Determine the resistivity of the metal from which the wire is made.
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resistivity = .................................................. Ω m [2]
(ii) Calculate the charge that passes through the wire in a time of 5.0 minutes.
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charge = ..................................................... C [2]
(iii) The free electrons (charge carriers) in the wire have an average drift speed of
0.16 mm s–1.
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Determine the number density of charge carriers in the metal.
number density = .................................................. m–3 [2]
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(c) The wire in (b) may be considered to be a fixed resistor. It is connected in series with a
thermistor to a battery that has negligible internal resistance.
(i) Use circuit symbols to complete Fig. 6.1 to show the circuit diagram of this arrangement.
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Fig. 6.1
[1]
(ii) Explain, without calculation, how the power dissipated in the wire changes as the
temperature of the thermistor is increased.
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[Total: 10]
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7 (a) Fig. 7.1 shows two resistors connected in series with a cell of electromotive force (e.m.f.)
1.50 V and internal resistance 0.28 Ω.
1.50 V
0.28 Ω
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1.0 Ω R
Fig. 7.1
One of the resistors has resistance 1.0 Ω. The other resistor has resistance R.
The terminal potential difference (p.d.) across the cell is 1.36 V.
(i) Show that the current I in the circuit is 0.50 A.
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[2]
(ii) Calculate the combined resistance of the two resistors.
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resistance = ...................................................... Ω [2]
(iii) Use your answer in (a)(ii) to determine resistance R.
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R = ...................................................... Ω [1]
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(b) The circuit in Fig. 7.1 is disconnected and the two resistors are reconnected to the cell, now
in parallel with each other.
(i) On Fig. 7.2, complete the circuit diagram to show this arrangement.
1.50 V
0.28 Ω
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Fig. 7.2
[1]
(ii) Explain, without calculation, whether the terminal p.d. across the cell is now less than,
equal to or greater than 1.36 V.
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[Total: 8]
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