Question

A 50Ω resistor is connected in parallel with an inductive reactance of 30Ω. A 20V signal is applied to the circuit. Find the line current in the circuit.

(a) 0.77∠-58.8⁰

(b) 0.77∠58.8⁰

(c) 0.88∠-58.8⁰

(d) 0.88∠58.8⁰

This question was posed to me during an internship interview.

Asked question is from Parallel Circuits topic in portion Complex Impedence of Network Theory

Answer 1

Right answer is (a) 0.77∠-58.8⁰

To explain I would say: Since the voltage across each element is the same as the applied voltage, the current in resistive branch is IR = VS/R = 20∠0⁰/50∠0⁰=0.4A. Current in the inductive branch is IL = VS/XL = 20∠0⁰/30∠90⁰= 0.66∠-90⁰. Total current is IT = 0.4-j0.66 = 0.77∠-58.8⁰.