A LevelPhysicsCIETopic Questions21. Alternating Currents21.1 Characteristics of Alternating Currents

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First teaching 2023

First exams 2025

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Characteristics of Alternating Currents (CIE A Level Physics)

Topic Questions

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1a
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For an alternating voltage, state what is meant by 

(i)
the peak voltage,
[1]
(ii)
the root mean square voltage.
[2]

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1b
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A generator produces an alternating voltage which can be described by the equation

V space equals space 150 space sin space open parentheses 200 straight pi t close parentheses

where V is measured in volts and t is in seconds.

For this alternating voltage, determine

(i)
the peak voltage,
[1]
(ii)
the r.m.s. voltage,
[1]
(iii)
the frequency.
[1]

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1c
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The alternating voltage is supplied across a 100 Ω resistor.

Calculate

(i)
the peak current and hence the r.m.s. current in the resistor,
[2]
(ii)
the mean power dissipated in the resistor,
[2]
(iii)
the peak power dissipated in the resistor.
[2]

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1d
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State the effect on the output voltage if the frequency of the generator is increased.

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2a
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Fig. 1.1a shows an alternating current generator with a rectangular coil rotating at a constant frequency in a uniform magnetic field.

11-2-ib-hl-sqs-easy-q2a-question

Fig. 1.1a

The graph in Fig. 1.1b shows how the output voltage V from the generator varies with time t.

11-2-ib-hl-sqs-easy-q2b-question

Fig. 1.1b

Using Fig. 1.1b, state the peak output voltage V subscript 0 of the generator.

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2b
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Calculate the root mean squared voltage V subscript r m s end subscript.

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2c
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The mean power output of the generator is 35 kW.

Calculate the root mean squared current I subscript r m s end subscript.

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2d
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Draw a line on the graph in Fig. 1.1b to show the Vrms.

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3a
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In rectification, a smoothing capacitor is often necessary.

State the meaning of

(i)
rectification,
[1]
(ii)
smoothing.
[1]

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3b
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Fig. 1.1a shows the voltage output from an alternating current supply.

ib-sq-11-3-qu-4b-1

Fig. 1.1a

Sketch the variation of time with output voltage during

 
(i)
half-wave rectification on Fig. 1.1b
 

ib-sq-11-3-qu-4b-2

Fig. 1.1b

[2]

(ii)
full-wave rectification on Fig. 1.1c
 

ib-sq-11-3-qu-4b-2

Fig. 1.1c

[2]

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3c
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A capacitor is placed in parallel with a resistive load to smooth the rectified voltage. The graph of the smoothed output voltage against time gives a 'ripple' shape as shown in Fig. 1.2.

ib-sq-11-3-qu-4c

Fig. 1.2

State how the 'ripples' in the graph can be reduced.

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3d
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Fig. 1.3a shows a diode bridge circuit. It is designed to allow current to flow in certain pathways depending on the input direct of the current.

21-1-3d-21-1-e-diode-bridge-circuit-1-cie-ial-sq

Fig. 1.3a

Draw the path of the current

(i)
on Fig. 1.3b

21-1-3d-21-1-e-diode-bridge-circuit-2-cie-ial-sq

Fig. 1.3b

[1]

(ii)
on Fig. 1.3c

21-1-3d21-1-e-diode-bridge-circuit-3-cie-ial-sq

Fig. 1.3c

[1]

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1a
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Fig. 1.1 below shows the graph of the voltage against time for a mains supply in the UK. 

7-10-s-q--q2a-hard-aqa-a-level-physics

Fig. 1.1

Using Fig. 1.1, draw a line to show the dc voltage that gives the same power as produced by the alternating waveform in the mains supply.

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1b
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Sketch a graph which shows how the power supplied by this voltage to a resistor with resistance of 300 Ω varies with time. 

Label the vertical axis as power and mark on both axes any significant values.

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1c
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The signal in Fig. 1.1 is connected to an oscilloscope. The screen's grid has a height of 8 squares and a width of 10 squares.

Describe how you would use the oscilloscope to display the alternating waveform in Fig. 1.1 so that four complete cycles are visible and occupy the full height of the screen.

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1d
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An electric oven is connected to the mains supply from part (a), using a cable with a non-negligible resistance. The cable connects the heating element in the oven to the mains supply. 

Explain why the rms voltage across the heating element in the oven will be less than the rms voltage calculated in part (a).

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2a
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Fig. 1.1 below shows a horizontal wire, held in tension between fixed points at P and Q. A short section of the wire is positioned between the pole pieces of a permanent magnet, which applies a uniform horizontal magnetic field at right angles to the wire. Wires connected to a circuit at P and Q allow an alternating current to be passed through the wire.

hq2

Fig. 1.1

(i)
Explain why the wire oscillates.

(5)

(ii)
The permanent magnet produces a uniform magnetic field of flux density 220 mT over a 55 mm length of the wire. Show that the maximum force on the wire is about 40 mN when there is an alternating current of rms value 2.4 A in it. 

(2)

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2b
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When modelling the motion of the wire between P and Q, a student says the wire at the midpoint of P and Q is displaced 2.0 cm from equilibrium as it oscillated, and it moves with an average speed of 0.16 m s−1. 

Write an expression for the current supplied to the wire at time t . You may leave a factor of π in your expression.

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2c
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In reality, the oscillations of the wire are not symmetrical. Explain why.

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1a
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A sinusoidal alternating voltage has a root-mean-square voltage of 5.1 V and a frequency of 40 Hz.  

The alternating voltage is applied across a resistor of resistance 1430 Ω. 

Calculate the mean power dissipated by the resistor in mW. 

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1b
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On Fig. 1.1, draw a smooth curve to show how the power P dissipated in the resistor varies with time t between t = 0 and t = 100 ms.

Assume that P = 0 when t = 0.

21-1-3b-m-power-time-graph-axis-sq-cie-a-level

Fig. 1.1

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1c
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The alternating voltage in (a) is applied to a piezoelectric crystal in air. 

State and explain

(i)
the effect this has on the air surrounding the crystal
[2]
(ii)
which quantity must change if the crystal were to be used in an ultrasound transducer.
[2]

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2a
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The output voltage V of an a.c. power supply varies sinusoidally with time t as shown in Fig. 1.1.

21-1-1b-m-a-c--graph-find-omega-sq-cie-a-levelFig. 1.1

Using Fig. 1.1, determine the equation for V in terms of t, where V is in volts and t is in seconds.

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2b
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Using Fig. 1.1, determine

(i)
the root-mean-square voltage V subscript r m s end subscript
[1]
(ii)
the mean voltage open angle brackets V close angle brackets
[1]

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2c
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The supply is connected to a 25 Ω resistor.

Calculate the mean power dissipated in the resistor. 

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3a
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Explain, by referring to the heating effect, what is meant by the root-mean-square (r.m.s.) value of an alternating current.

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3b
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An alternating current supply is connected in series with a resistor R.

The value of the current I, in amps, varies with time t, in seconds, according to

I space equals space 15 space sin space 60 t

For the current through the resistor, determine

(i)
the peak current
[1]
(ii)
the r.m.s. current
[1]
(iii)
the frequency.
[1]

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3c
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To prevent overheating, the mean power dissipated in resistor R must not exceed 1.0 kW.

Calculate the minimum resistance of R.

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