Answer to Question #165733 in Electric Circuits for Julie

Question

Two coils A and B are connected in series across a 110V, 60Hz supply. The resistance of coil A is 2  and inductance of coil B is 0.004H. If the input from the supply is 2.4kW and 1.8kVAR, find the inductance of coil A and resistance of coil B. Also calculate the voltage across each coil.

Answer 1

Voltage applied, $V = 110 V$

Frequency, $f = 60 Hz$

The resistance of coil A, $R_A = 2 \Omega$

Then it's inductance, $R_A = 2\pi f L_A \implies L_A = \frac{R_A}{2\pi f} = 0.0053 H$

Inductance of coil B, $L_B = 0.004H$

Resistance of coil B, $R_B = 2\pi fL_B = (2\times \pi \times 60 \times0.004) = 1.5 \Omega$

Since these are in series, so current in A and B will be same. Current in the circuit is given by, $I = \frac{V}{R} = \frac{V}{R_A+R_B}=\frac{110}{2+1.5} = \frac{110}{3.5} A$

Voltage across A, $V_A = IR_A = \frac{110}{3.5}\times 2 = 62.86 V$

Voltage across B, $V_B=IR_B =\frac{110}{3.5}\times 1.5 = 47.14V$