Page 474 - Physics Coursebook 2015 (A level)

Cambridge International A Level Physics
Summary
■■ A sinusoidal alternating current can be represented by I = I0 sin ωt, where I0 is the peak value of the current.
■■ The root-mean-square value of an alternating current is that steady current which delivers the same average power as the a.c. to a resistive load; for a sinusoidal a.c.,
Irms = I0 . 2
■■ Electrical power is usually transmitted at high voltages; this allows the current to be reduced, and so resistive losses are lower.
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Transformers are used to change an alternating voltage. The voltage is stepped up or down in proportion to the turns ratio of the transformer.
For a transformer, Vs = Ns . If it is 100% efficient, then VpIp = VsIs. Vp Np
Diodes are used to convert a.c. to d.c. A single diode gives half-wave rectification. A bridge of four diodes gives full-wave rectification. A capacitor smoothes the rectified voltage.
End-of-chapter questions
1 Write down a general expression for the sinusoidal variation with time t of:
a an alternating voltage V [1]
b an alternating current I (you may assume that I and V are in phase) [1]
c the power P dissipated due to this current and voltage. [1]
2 The value in amps of an alternating current is represented by the equation I = 2 sin (50πt).
a What is the peak value of the current? [1]
b What is the frequency of the supply? [2]
c Sketch a graph to show two cycles of the variation of current with time. Mark the axes with suitable values. [2]
d Calculate Irms, the r.m.s. value of current, and mark this on your graph. [1]
e Find two values of t at which I = Irms. [3]
3 The a.c. mains of 240 V r.m.s. is connected to the primary coil of a transformer, which contains 1200 turns. The r.m.s. output of the transformer is 6.0 V.
a Calculate the number of turns on the secondary coil. [1]
b A resistance of 6.0 Ω is connected across the secondary coil. Calculate:
i the average power dissipated in the resistor [1]
ii the peak current in the primary coil. [3]
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