(a) State the laws of electromagnetic induction. (b) (i) Describe a simple experiment to show how an induced e.m.f, can be produced; (ii) State two factors ...

(a) Laws of electromagnetic induction

• Faraday's law: whenever there is a change in the magnetic flux linking a circuit, an e.m.f. is induced, and the magnitude of the induced e.m.f. is directly proportional to the rate of change of the magnetic flux linkage.
• Lenz's law: the direction of the induced current is always such that it opposes the change producing it.

(b)(i) Simple experiment

Connect a coil of wire to a sensitive galvanometer. When a bar magnet is pushed into (or pulled out of) the coil, the galvanometer deflects, showing that an e.m.f. (and current) is induced. When the magnet is held still there is no deflection.

(b)(ii) Two factors on which the induced e.m.f. depends

• The rate at which the magnetic flux changes (the speed of the magnet).
• The number of turns on the coil (and the strength of the magnet).

(c) r.m.s. value of an alternating current

The root-mean-square value of an alternating current is the value of the steady direct current that would dissipate heat in a given resistor at the same rate as the alternating current does.

(d)(i) Meaning of the symbols in \( I = I_o \sin \omega t \)

• \( I \) is the instantaneous value of the current at time t.
• \( I_o \) is the peak (maximum) value of the current.
• \( \omega \) is the angular frequency, \( \omega = 2\pi f \).
• \( \omega t \) is the phase angle of the current at time t.

(d)(ii) Instantaneous value

Peak value: \( I_o = I_{rms}\sqrt{2} = 15.0 \times 1.414 = 21.2\,\text{A} \).

At phase angle \( \omega t = 30^\circ \):

\[ I = I_o \sin 30^\circ = 21.2 \times 0.5 = 10.6\,\text{A} \]

The instantaneous current is about 10.6 A.