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Show that the torque produced in a permanent-magnet moving-coil instrument is proportional to the area of the moving coil. A moving-coil voltmeter gives full-scale deflection with a current of 5 mA. The coil has 100 turns, effective depth of 3 cm and width of 2.5 cm. The controlling torque of the spring is 0.5 cm for full-scale deflection. Estimate the flux density in the gap.

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The full-scale deflecting torque is Td = NBIA N-m 

where I is the full-scale deflection current ; 

I = 5mA = 0.005A 

Td = 100 × B × 0.005 × (3 × 2.5 × 10−4 ) = 3.75 × 10−4 B N-m 

The controlling torque is 

Tc = 0.5 g-cm = 0.5 g. wt.cm 

= 0.5 × 10−3 × 10−2 kg wt-m 

= 0.5 × 10−5 × 9.8 

= 4.9 × 10−5 N-m 

For equilibrium, the two torques are equal and opposite. 

∴ 4.9 × 10−5 = 3.75 × 10−4

∴ B = 0.13 Wb/m

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