Question

An 75.0 resistor and a 200 mH inductor are connected in parallel across a 105 V (rms), 60.0 Hz source.

(a) What is the rms current in the resistor? Find in Amps

(b) By what angle does the total current lead or lag behind the voltage?

The current lags the voltage by (find degrees)

Answer 1

here,

R = 75 ohm

L = 200 mH

L = 0.2 H

voltage , V = 105 V

frequency , f = 60 Hz

A)

Current in resistor = (105 V) / (75 Ohms) = 1.4 Amps (RMS)

B)

Inductive reactance: 2 Pi f L = 2 Pi (60 Hz)(0.2 H) = 75.4 Ohms

Impedance of parallel combination

Z = (75.4 i)(75) / ( 75.4i + 50 )

Z = 136.41 - 88.77i = 162.75 Ohms at 62.57 degrees

The total current is therefore (105 V) / Z = 0.64 Amps and cureent lead the volatge by 62.57 degrees