Answer to Question 10 
A wattmeter has a coil consisting of 40 turns of very thin copper wire on a very light rectangular former 1.0 cm × 2.0 cm. It is held in place on a shaft where the friction is negligible. Its resistance is 200 W. Its motion is opposed by two very fine hair springs of which the torsion constant is 1.5 mN m rad^{1} for each spring. The coil is connected to the supply through a multiplier of which the resistance is 50 kW.
The magnetic field is formed by a coil consisting of 30 turns in a length of 5 cm. The core of the electromagnet has relative permeability of 200.
The load takes a power of 250 W
Calculate the angle through which the needle turns.

Work out the area: A = 0.010 m × 0.020 m = 2.0 × 10^{4} m^{2}. Work out the number of turns per metre: n = 30 ÷ 0.050 m = 600 m^{1}. Two springs, so k = 2 × 1.5 × 10^{6} N m rad^{1} = 3.0 × 10^{6} N m rad^{1} Formula:
q = (4p × 10^{7} × 200 × 600 × 2.0 × 10^{4} × 40 × 250) ÷ (3.0 × 10^{6} × 50200) = 0.637 rad (= 37^{o}) 