Edexcel A-Level Physics AS: Electric Circuits

[Maximum number: 13]

The circuit contains three identical resistors and switches X and Y. Each resistor is wire of diameter $0.181\,\mathrm{mm}$ and length $55.0\,\mathrm{cm}$ , with resistivity $1.10\times10^{-6}\,\Omega\,\mathrm{m}$ at room temperature.

Figure for Question 1 — Edexcel A-Level Physics AS

(a)

Show that the resistance of one resistor at room temperature is about $24\,\Omega$ .

[ 3 ]

Use $A=\pi r^2$ and $R=\rho l/A$ .
$A=\pi(0.0905\times10^{-3})^2=2.57\times10^{-8}\,\mathrm{m^2},$ $R=\frac{(1.10\times10^{-6})(0.550)}{2.57\times10^{-8}}=23.5\,\Omega.$

(b)

A student suggests that the maximum power output from the resistors in this circuit will be greater than 12 W .

Assess whether the student's suggestion is correct.

[ 4 ]

Maximum power occurs at minimum total resistance. With X and Y closed, $R_{tot}=(1/47+1/23.5)^{-1}=15.7\,\Omega$ . Thus $P=V^2/R=12.0^2/15.7=9.2\,\mathrm{W}$ , less than $12\,\mathrm{W}$ , so the suggestion is incorrect.

(c)

Switch X was open and switch Y was closed.

[ 6 ]

(i)

Calculate the number of conduction electrons passing through the resistor each second immediately after switch Y is closed.

Number of electrons =

[ 3 ]

Immediately after closing Y, $I=V/R=12.0/23.5=0.511\,\mathrm{A}$ . In one second $Q=It=0.511\,\mathrm{C}$ , so
$N=Q/e=0.511/(1.60\times10^{-19})=3.2\times10^{18}.$

(ii)

After switch Y had been closed for a few minutes, the power dissipated by the resistor decreased.

Explain why.

[ 3 ]

The resistor temperature rises, so its resistance rises. Since $P=V^2/R$ for fixed supply voltage, the dissipated power decreases.

[Maximum number: 1]

The cell in a solar-powered lamp stores 6.0 kJ of energy.
The lamp is switched on and the cell discharges fully. The cell has a constant e.m.f. of 1.5 V.
Which of the following is the charge flowing through the lamp during discharge?

A

250 C

B

900 C

C

4000 C

D

9000 C

[Maximum number: 10]

A student set up the circuit shown to investigate the properties of a negative temperature coefficient thermistor.

Figure for Question 3 — Edexcel A-Level Physics AS

The power supply has negligible internal resistance.

(a)

Show that the voltmeter reading was about 6 V .
ammeter reading $=23 \mathrm{~mA}$

[ 3 ]

ai

$\text { Use of } \frac{1}{R}=\frac{1}{500 \Omega}+\frac{1}{600 \Omega}$

Use of V=I R

Voltmeter reading $=6.3(\mathrm{~V})$

Example of calculation
$\begin{aligned} & \frac{1}{R_{\text {parallel }}}=\frac{1}{500 \Omega}+\frac{1}{600 \Omega}, \text { so } R_{\text {parallel }}=273 \Omega & V=I R=23.0 \times 10^{-3} \mathrm{~A} \times 273 \Omega=6.28 \mathrm{~V} \end{aligned}$

(b)

Calculate the power dissipated by the thermistor.

Power =

[ 3 ]

aii

p.d. across thermistor $=12 \mathrm{~V}-6.3 \mathrm{~V}$ (allow ecf from ai)

Use of P=V I (allow use of $P=I^{2} R$ or $P=V^{2} / R$ )
$P=0.13 \mathrm{~W}$

Example of calculation

p.d. across thermistor $=12.0 \mathrm{~V}-6.3 \mathrm{~V}=5.7 \mathrm{~V}$ $\begin{aligned} & P=V I=5.7 \mathrm{~V} \times 23 \times 10^{-3} \mathrm{~A} & P=0.13 \mathrm{~W} \end{aligned}$

(c)

The student decreases the temperature of the thermistor.

Explain the effect of decreasing the temperature of the thermistor on the ammeter and voltmeter readings.

[ 4 ]

[Maximum number: 3]

The circuit contains three identical resistors and switches X and Y. Each resistor is wire of diameter $0.181\,\mathrm{mm}$ and length $55.0\,\mathrm{cm}$ , with resistivity $1.10\times10^{-6}\,\Omega\,\mathrm{m}$ at room temperature.

Figure for Question 4 — Edexcel A-Level Physics AS

Switch X was open and switch Y was closed.

Calculate the number of conduction electrons passing through the resistor each second immediately after switch Y is closed.

Number of electrons =

Immediately after closing Y, $I=V/R=12.0/23.5=0.511\,\mathrm{A}$ . In one second $Q=It=0.511\,\mathrm{C}$ , so
$N=Q/e=0.511/(1.60\times10^{-19})=3.2\times10^{18}.$

[Maximum number: 3]

A student set up the circuit shown to investigate the properties of a negative temperature coefficient thermistor.

Figure for Question 5 — Edexcel A-Level Physics AS

The power supply has negligible internal resistance.

Show that the voltmeter reading was about 6 V .
ammeter reading $=23 \mathrm{~mA}$

ai

$\text { Use of } \frac{1}{R}=\frac{1}{500 \Omega}+\frac{1}{600 \Omega}$

Use of V=I R

Voltmeter reading $=6.3(\mathrm{~V})$

Example of calculation
$\begin{aligned} & \frac{1}{R_{\text {parallel }}}=\frac{1}{500 \Omega}+\frac{1}{600 \Omega}, \text { so } R_{\text {parallel }}=273 \Omega & V=I R=23.0 \times 10^{-3} \mathrm{~A} \times 273 \Omega=6.28 \mathrm{~V} \end{aligned}$

[Maximum number: 3]

Drivers use car headlights to emit light in dark conditions.
The graph shows how current I varies with potential difference V for a car headlight.

Figure for Question 6 — Edexcel A-Level Physics AS

The headlight will emit light when it dissipates at least 35 W of power.

In a car, two headlights are connected in parallel with a 12.0 V battery. The battery has negligible internal resistance.

Explain the advantages of connecting the headlights in parallel with the battery rather than in series.

[Maximum number: 3]

Drivers use car headlights to emit light in dark conditions.
The graph shows how current I varies with potential difference V for a car headlight.

Figure for Question 7 — Edexcel A-Level Physics AS

The headlight will emit light when it dissipates at least 35 W of power.

In a car, two headlights are connected in parallel with a 12.0 V battery. The battery has negligible internal resistance.

A student writes the following statement.

When connected to the 12.0 V battery, the combined resistance of two headlights in parallel is one quarter of the combined resistance of two headlights in series.

Deduce whether the student is correct.
Your answer should include calculations using data from the graph.

From the graph, one headlight at $12.0\,\mathrm{V}$ takes $4.6\,\mathrm{A}$ , so $R=V/I=2.61\,\Omega$ and two in parallel have $R_T=1.30\,\Omega$ . At $6.0\,\mathrm{V}$ , one takes about $3.2\,\mathrm{A}$ , so two in series have $R_T=2(6.0/3.2)=3.76\,\Omega$ . The ratio is 3.76/1.30=2.9, not 4, so the student is incorrect.

[Maximum number: 3]

Drivers use car headlights to emit light in dark conditions.
The graph shows how current I varies with potential difference V for a car headlight.

Figure for Question 8 — Edexcel A-Level Physics AS

The headlight will emit light when it dissipates at least 35 W of power.

Determine the minimum potential difference for which the headlight will emit light.
(3)

Minimum potential difference = V

[Maximum number: 1]

The current-potential difference (p.d.) graph for a diode is shown.

Figure for Question 9 — Edexcel A-Level Physics AS

Which of the following statements is correct for this diode?

A

This diode does not conduct in the reverse direction.

B

The resistance of this diode in the reverse direction is infinite.

C

The resistance of this diode decreases when the p.d. is above 0.7 V .

D

This diode does not conduct when the p.d. is below 0.7 V .

[Maximum number: 3]

The circuit contains three identical resistors and switches X and Y. Each resistor is wire of diameter $0.181\,\mathrm{mm}$ and length $55.0\,\mathrm{cm}$ , with resistivity $1.10\times10^{-6}\,\Omega\,\mathrm{m}$ at room temperature.

Figure for Question 10 — Edexcel A-Level Physics AS

Show that the resistance of one resistor at room temperature is about $24\,\Omega$ .

Use $A=\pi r^2$ and $R=\rho l/A$ .
$A=\pi(0.0905\times10^{-3})^2=2.57\times10^{-8}\,\mathrm{m^2},$ $R=\frac{(1.10\times10^{-6})(0.550)}{2.57\times10^{-8}}=23.5\,\Omega.$

[Maximum number: 2]

A student carried out an experiment to determine the resistivity of nichrome wire. Her circuit included an ammeter, a voltmeter and a variable resistor.

Complete the circuit diagram for this experiment.

Figure for Question 11 — Edexcel A-Level Physics AS

[Maximum number: 3]

Drivers use car headlights to emit light in dark conditions.
The graph shows how current I varies with potential difference V for a car headlight.

Figure for Question 12 — Edexcel A-Level Physics AS

The headlight will emit light when it dissipates at least 35 W of power.

The headlights are connected using copper wire. The current is $4.60\,\mathrm{A}$ . Calculate the drift velocity of electrons.

Number density $n=8.49\times10^{28}\,\mathrm{m^{-3}}$

Resistivity $\rho=1.72\times10^{-8}\,\Omega\,\mathrm{m}$

Resistance per unit length $R/l=1.75\times10^{-2}\,\Omega\,\mathrm{m^{-1}}$ .

From $R=\rho l/A$ , using resistance per unit length, $A=\frac{\rho}{R/l}=\frac{1.72\times10^{-8}}{1.75\times10^{-2}}=9.83\times10^{-7}\,\mathrm{m^2}.$ Then $v=\frac{I}{nqA}=\frac{4.60}{(8.49\times10^{28})(1.60\times10^{-19})(9.83\times10^{-7})}=3.4\times10^{-4}\,\mathrm{m\,s^{-1}}.$

[Maximum number: 1]

'Resistivity paper' is paper covered with a thin layer of carbon.
The distance between the ends of a piece of resistivity paper is 12.0 cm . The resistivity paper is 4.2 cm wide as shown.

Figure for Question 13 — Edexcel A-Level Physics AS

The resistance between the ends of the resistivity paper is $8.8 \Omega$ .

A student connected the ends of the resistivity paper to a cell of e.m.f. 1.5 V and a voltmeter, as shown.

The connection to the right-hand terminal of the voltmeter was moved to a distance of 3.0 cm from the left-hand side of the resistivity paper.

Determine the reading on the voltmeter.

Reading on voltmeter =

[Maximum number: 3]

A student investigated the behaviour of a thermistor using the circuit shown in the diagram.

She heated the thermistor to 100 °C and measured the potential difference V across it. She decreased the temperature θ and recorded further measurements of V and θ until the temperature reached 10 °C.

Figure for Question 14 — Edexcel A-Level Physics AS

The student plotted a graph of her measurements of V and θ.

Calculate the resistance of the thermistor at a temperature of 0 °C.

Resistance =

[Maximum number: 3]

Resistors are included in circuits that are used as potential dividers.

The circuit shown below includes a light dependent resistor (LDR). The battery has no internal resistance.

Figure for Question 15 — Edexcel A-Level Physics AS

In normal daylight, this particular type of LDR has a resistance of $670\,\Omega$ .

Calculate the power dissipated in the fixed resistor in normal daylight.

resistance of fixed resistor $=8.00\,\mathrm{k}\Omega$

ci

Use of V=I R to determine circuit current

Use of $P=I^{2} R$ or $P=V^{2} / R$ or P=V I

$P=1.5 \times 10^{-2} \mathrm{~W}$

Or

Ratio of resistances used to calculate p.d. across R

Use of $P=V^{2} / R$ $P=1.5 \times 10^{-2} \mathrm{~W}$

Example of calculation

$\mathrm{I}=12.0 \mathrm{~V} /(8000+670 \Omega)=1.38 \times 10^{-3} \mathrm{~A}$ $\mathrm{P}=\left(1.38 \times 10^{-3} \mathrm{~A}\right)^{2} \times 8000=0.015 \mathrm{~W}$

(1)

(1)

(1)

(1)

(1)

(1)

[Maximum number: 3]

'Resistivity paper' is paper covered with a thin layer of carbon.
The distance between the ends of a piece of resistivity paper is 12.0 cm . The resistivity paper is 4.2 cm wide as shown.

Figure for Question 16 — Edexcel A-Level Physics AS

The resistance between the ends of the resistivity paper is $8.8 \Omega$ .

A student connected the ends of the resistivity paper to a cell of e.m.f. 1.5 V and a voltmeter, as shown.

The reading on the voltmeter was 1.4 V .

Calculate the internal resistance of the cell.

Internal resistance =

[Maximum number: 7]

A student carries out an experiment to determine the e.m.f. $\varepsilon$ and internal resistance r of an electrical cell, using a circuit containing an ammeter and a voltmeter.

(a)

Draw a diagram of a circuit that can be used for this experiment.

[ 3 ]

(b)

The student plotted a graph of the terminal potential difference V of the cell against the current I in the cell, as shown. Explain how the e.m.f. $\varepsilon$ and internal resistance r can be determined from this graph.

Figure for Question (b) — Edexcel A-Level Physics AS

[ 4 ]

Conservation of energy gives $\varepsilon=V+Ir$ , or $V=\varepsilon-Ir$ . Comparing with y=mx+c, the y-intercept is the e.m.f. $\varepsilon$ , and the negative of the gradient is the internal resistance r.

[Maximum number: 3]

The circuit contains three identical resistors and switches X and Y. Each resistor is wire of diameter $0.181\,\mathrm{mm}$ and length $55.0\,\mathrm{cm}$ , with resistivity $1.10\times10^{-6}\,\Omega\,\mathrm{m}$ at room temperature.

Figure for Question 18 — Edexcel A-Level Physics AS

Switch X was open and switch Y was closed.

After switch Y had been closed for a few minutes, the power dissipated by the resistor decreased.

Explain why.

The resistor temperature rises, so its resistance rises. Since $P=V^2/R$ for fixed supply voltage, the dissipated power decreases.

[Maximum number: 4]

Resistors are included in circuits that are used as potential dividers.

The circuit shown below includes a light dependent resistor (LDR). The battery has no internal resistance.

Figure for Question 19 — Edexcel A-Level Physics AS

As the light intensity incident upon the LDR decreases, the power dissipated in the fixed resistor decreases.

Explain why the power in the fixed resistor decreases. Your answer should include reference to the electrons in the LDR.

Edexcel A-Level Physics AS 2.4 Electric Circuits Questions

Exam points

Covered syllabus points

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (c)

Question (i)

Question (ii)

Question 2

Question 3

Question (a)

Question (b)

Question (c)

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question (a)

Question (b)

Question 18

Question 19