# Maxwell bridge is used to measure

Maxwell bridge is used to measure

#### SOLUTION

A Maxwell bridge is a modification to a Wheatstone bridge used to measure an unknown inductance (usually of low Q value) in terms of calibrated resistance and inductance or resistance and capacitance.

As in the balanced condition of the Wheatstone bridge product of opposite arms, resistance is equal i.e

R1R3 = R2R4

In Maxwell AC bridge in the two arms, there are two pure resistances so that for balance relations, the phase balance depends on the remaining two arms.

For the balanced condition of the Maxwell AC bridge

Z1Z3 = Z2Z4

Where Z1 is the unknown Impedance

Z1 = R1 + JX1 = R1 + JωL1

Z4 is the know Impedance

Z4 = R4 + JX4 = R4 + JωL4

R2 and R3 = Known pure resistance

∴ (R1 + JωL1)R3 = (R4 + JωL4)R2

Equating real and Imaginary part

R1R3 = R2R4

&

ωL1R3 = ωL4R2
L1R3 = L4R2

Hence, the unknown self-inductance can be measured in terms of the known inductance L4 and the two resistors. Resistive and reactive terms balance independently and the conditions are independent of frequency. This bridge is often used for measuring the iron losses of the transformers at audio frequency.

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