Question

In the circuit given below, the value of Z which would cause parallel resonance at 500 Hz is ___________

(a) 125 mH

(b) 34.20 μF

(c) 2 μF

(d) 0.05 μF

I had been asked this question by my college professor while I was bunking the class.

I want to ask this question from Problems Involving Standard Time Functions in section Application of the Laplace Transform in Circuit Analysis of Network Theory

Answer 1

The correct answer is (d) 0.05 μF

The best explanation: At resonance the circuit should have unity power factor

Hence, Z should be capacitive.

Now, \(\frac{1}{jLω} + \frac{1}{1/jCω}\) = 0

Or, \(\frac{-1}{jLω}\) + jCω = 0

∴ C = \(\frac{1}{L × ω^2} = \frac{1}{2 × (2π × 500)^2}\)

= 0.05 μF.