Characteristics of Alternating Currents (Cambridge (CIE) A Level Physics)

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. 

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.

Fig. 1.1

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]

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

Fig. 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.

Using Fig. 1.1, determine

(i) the root-mean-square voltage

[1]

(ii) the mean voltage

[1]

The supply is connected to a 25 Ω resistor.

Calculate the mean power dissipated in the resistor. 

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

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

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

For the current through the resistor, determine

(i) the peak current

[1]

(ii) the r.m.s. current

[1]

(iii) the frequency.

[1]

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

Calculate the minimum resistance of R.

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

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.

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.

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.

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).

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.

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]

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.

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