(a) Define: (i) reactance; (ii) impedance in an a.c. The diagram here illustrates an a.c. generator. When the coil is rotated, an e.m.f is induced in the co...

Answer Details

(a) Definitions

• Reactance is the opposition offered to the flow of alternating current by an inductor or a capacitor, arising from the induced back-e.m.f (inductor) or stored charge (capacitor). It is measured in ohms and, unlike resistance, does not dissipate energy.
• Impedance is the total opposition to the flow of alternating current in a circuit, being the combined effect of resistance and reactance. It is measured in ohms, \(Z=\sqrt{R^2+X^2}\).

(b) The a.c. generator (shown with the coil between the N and S poles, the slip rings and the load)

1. Why an e.m.f. is induced: As the coil rotates in the magnetic field between the N and S poles, the magnetic flux linking the coil changes continuously. By Faraday's law, a changing flux linkage induces an e.m.f. in the coil; the e.m.f. is greatest when the coil moves parallel to the field (cutting flux fastest) and zero when it moves perpendicular to it.
2. Purpose of the slip-rings: They provide a continuous sliding electrical contact between the ends of the rotating coil and the external circuit (through the brushes), so that the induced alternating e.m.f. is delivered to the load without the connecting wires twisting.
3. Law for the direction of the induced current: Fleming's right-hand (dynamo) rule. Holding the thumb, first finger and second finger of the right hand mutually at right angles, the First finger points along the Field (N to S), the Thumb along the Thrust (motion of the conductor), and the seCond finger then gives the direction of the induced Current.
4. Two ways to increase the induced e.m.f.: increase the number of turns on the coil; rotate the coil faster (higher speed of rotation). (Others: use a stronger magnet, or a larger coil area / soft-iron core.)

(c) Energy transformed by a 12 V, 6 W lamp in 5 minutes

Power \(P=6\text{ W}\); time \(t=5\times60=300\text{ s}\).

The lamp transforms 1800 J of electrical energy in 5 minutes.