Question

For the series resonant circuit given below, the value of the equivalent impedance of the circuit is ________

(a) 55 Ω

(b) 47 Ω

(c) 64 Ω

(d) 10 Ω

I got this question in a national level competition.

I want to ask this question from Problems of Parallel Resonance Involving Quality Factor topic in section Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Right answer is (b) 47 Ω

Easy explanation: Resonant Frequency, \(\frac{1}{2π\sqrt{LC}} \)

= \(\frac{1}{6.28\sqrt{(4.7×10^{-3})(0.001×10^{-6})}}\)

= \(\frac{1}{6.28\sqrt{4.7×10^{-12}}}\)

= \(\frac{1}{1.362×10^{-5}}\) = 73.412 kHz

Inductive Reactance, XL = 2πfL = (6.28) (73.142 × 10^3)(4.7 × 10^-6)

= 2.168 kΩ

Capacitive Reactance, XC = \(\frac{1}{2πfC} = \frac{1}{(6.28)(73.142×10^3)(0.001×10^{-6})}\)

= \(\frac{1}{4.613×10^{-4}}\) = 2.168 kΩ

We see that, XC = XL are equal, along with being 180° out of phase.

Hence the net reactance is zero and the total impedance equal to the resistor.

∴ ZEQ = R = 47 Ω.