Question

The arms of an a.c. Maxwell bridge are arranged as follows: AB and BC are non-reactive resistors of 100 Ω each, DA is a standard variable reactor L1 of resistance 32.7 Ω and CD comprises a standard variable resistor R in series with a coil of unknown impedance. Balance was obtained with L1 = 47.8 mH and R = 1.36 Ω . Find the resistance and inductance of the coil.

Answer 1

The a.c. bridge is shown in Fig..

Since the products of the resistances of opposite arms are equal

∴ 32.7 x 100 = (1.36 + R4)100

∴ 32.7 = 1.36 + R4 or R4 = 32.7 - 1.36 = 31.34Ω

Since L1 x 100 = L4 x 100

∴ L4 = L1 = 47.8 mH

or because time constants are the same, hence

L1/32.7 = L4/(31.34 + 1.36)

∴ L4 = 47.8 mH