Question

In an AC circuit, resistance 50 Ω, inductance 0.3 H and capacitance 15 μF is connected to an AC voltage source 25 V, 50 Hz. Determine the impedance in the circuit.

(a) 110 ohm

(b) 100 ohm

(c) 125 ohm

(d) 140 ohm

This question was posed to me in an international level competition.

The question is from Kirchhoff’s Laws and Network Solution topic in portion Network Theorems Applied to AC Networks of Basic Electrical Engineering

Answer 1

The correct answer is (c) 125 ohm

Explanation: Z^2 = R^2+(XL-XC)^2, XL=2πfL,  XC=1/(2πfC)    f=50Hz and L=0.3H and C=15 μF

XL=2π(50)(0.3)= 94.25 ohm .

XC=1/(2π*50*15*10^-6) =  212.21 ohm.

Z^2=50^2+(212.21-94.25)^2=15625

Z = 125 ohm.