Answer to Question 10

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A watt-meter 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 m2.

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 (= 37o)