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 ΩI 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

For the series resonant circuit given below, the value of the equivale

1.	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 ΩI 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» 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.

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