Maxwell’s inductance bridge

The four arms of Maxwell’s inductance bridge are; Arm AB contains an Inductive coil of inductance L1 having resistance R1. Arms BC and CD contain non-inductive resistances of 200Ω and 100Ω respectively. Arm AD contains standard inductor of inductance L2 and resistance R2. Balance is obtained when L2=50mH and R2=2Ω. Find L1, R1 and Q factor for f= 50 Hz.

Correct result:

L1 =  0.1 H
R1 =  4
Q =  7.854

Solution:

R3=200 Ω R4=100 Ω L2=50/1000=120=0.05 H R2=2 Ω  U1=Z1 I1 U2=Z2 I2  U3=R3 I1 U4=R4 I2  U1=U2;U3=U4 Z1 I1=Z2 I2 R3 I1=R4 I2  Z1=R1+jωL1 Z2=R2+jωL2  (R1+jωL1) I1=(R2+jωL2) I2 I1=R4/R3 I2  (R1+jωL1) R4/R3 I2=(R2+jωL2) I2 (R1+jωL1) R4/R3=(R2+jωL2)  jωL1 R4/R3=jωL2 L1 R4/R3=L2  L1=L2 R3R4=0.05 200100=110=110 H=0.1 H
R1 R4/R3=R2  R1=R2 R3R4=2 200100=4 Ω
f=50 Hz ω=2π f=2 3.1416 50314.1593  Q=ω L1R1=314.1593 0.14=7.854



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