Question

For the circuit given below, the current I in the circuit is ________

(a) –j1 A

(b) J1 A

(c) Zero

(d) 20 A

This question was posed to me in an online quiz.

The origin of the question is Advanced Problems on Network Theory in chapter Network Theory and Complex Circuit Diagram of Network Theory

Answer 1

Correct answer is (a) –j1 A

The best I can explain: XEQ = sL + \(\frac{R×1/sC}{R+1/sC} = sL + \frac{R}{1+sRC}\)

IO = \(\frac{V}{X_{EQ}}\)

∴ I = \(\frac{X_C}{X_C+R}\) IO

= \(\frac{1/sC}{\frac{1}{sC}+R} × \frac{V}{\frac{sL(1+sRC)+R}{(1+sRC)}}\)

= \(\frac{1}{1+sRC} × \frac{V}{\frac{sL(1+sRC)+R}{(1+sRC)}}\)

= \(\frac{V}{sL(1+sRC)+R}\)

= \(\frac{V}{j×10^3×20×10^{-3} (1+j×10^3×50×10^{-6}+1)}\)

= \(\frac{V}{20j(1+j50×10^{-3})+1}\)

= \(\frac{V}{20j-1+1} = \frac{20}{20j}\) = -j1 A.