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 a 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 answer:

L1 =  0.1 H
R1 =  4
Q =  7.854

Step-by-step explanation:

R3=200 Ω R4=100 Ω L2=50/1000=201=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 + j ω L1 Z2 = R2 + j ω L2  (R1 + j ω L1)   I1 = (R2 + j ω L2)  I2 I1 = R4/R3   I2  (R1 + j ω L1)    R4/R3   I2 = (R2 + j ω L2)  I2 (R1 + j ω L1)    R4/R3 = (R2 + j ω L2)  j ω L1    R4/R3 = j ω L2 L1    R4/R3 = L2  L1=L2 R4R3=201 100200=20 1001 200=2000200=101 H=0.1 H
 R1    R4/R3 = R2  R1=R2 R4R3=2 100200=1002 200=100400=4 
f=50 Hz ω=2π f=2 3.1416 50314.1593  Q=ω R1L1=ω 4101=7.854

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