Question

A coil of inductance 120 mH and unknown resistance and a 1.0 μF capacitor are connected in series with an alternating emf of frequency 950 Hz. If the phase constant between the applied voltage and the current is 78°, what is the resistance of the coil?

Answer 1

Given Data

Inductance L = 120 mH = 120 * 10 ^ -3 H

Capacitance C = 1.0 μF = 1.0 * 10 ^ -6 F

Frequency f = 950 Hz

Phase constant φ = 78 degrees

Solution :-

Inductive reactance X= Lw = L * ( 2(pi) f )

= (120 * 10 ^ -3 ) * [ 2(pi) * 950 ]

= 715.92 ohm

Capacitive reactance X ‘ = 1 / C(2(pi) f)

= 1 / (1.0 * 10 ^ -6) [2(pi) * 950 ]

                                        = 167.62 ohm

We know tan φ = ( X - X') / R

= ( 715.92 - 167.62) / R

                        = 548.30 / R

R = 548.30 / tan φ

= 548.30 / tan 78

= 116.66 ohm