Question

A moving-coil milli voltmeter has a resistance of 20Ω and full-scale deflection of 120 is reached when a potential difference of 100 mV is applied across its terminals. The moving coil has the effective dimensions of 3.1 cm × 2.6 cm and is wound with 120 turns. The flux density in the gap is 0.15 Wb/m2 . Determine the control constant of the spring and suitable diameter of copper wire for coil winding if 55% of total instrument resistance is due to coil winding. ρ for copper = 1.73 × 10−6 Ω cm.

Answer 1

Full-scale deflection current is = 100/20 = 5 mA

Deflecting torque for full-scale deflection of 120 is

Td = NBIA = 120 × 0.15 × (5 × 10−3 ) × (3.1 × 2.6 × 10−4) = 72.5 × 10−6 N-m

Control constant is defined as the deflecting torque per radian (or degree) or deflection of moving coil. Since this deflecting torque is for 120° deflection.

Control constant = 72.5 × 10−6 /120 = 6.04 × 10−7 N-m/degree

Now, resistance of copper wire = 55% of 20 Ω = 11 Ω

Total length of copper wire = 120 × 2 (3.1 + 2.6) = 1368 cm

Now R = ρl/A

∴ A = 1.73 × 10−6 × 1368/11 = 215.2 × 10−6 cm2

∴ π d2 /4 = 215.2 × 10−6

∴ d = √((215 x 4 x 10-6)/π) = 16.55 × 10−3 cm = 0.1655 mm