In the given circuit, the magnitude of VL and VC are twice that of VR. Given that f = 50 Hz, the inductance of the coil is 1/Kπ mH. The value of K is ____________. Numerical answer type. Work it out, then open the answer.

Answer: 0. VL = VC means XL = XC: resonance, so Z = R = 5 Ω. I = 220/5 = 44 A, VR = 220 V, VL = 2VR = 440 V. XL = 440/44 = 10 Ω ⇒ L = (10)/(2π × 50) = (1)/(10π) H = (100)/(π) mH 1/Kπ = (100)/(π) ⇒ K = 0.01, which rounds to 0 as an integer answer.

In the given circuit, the magnitude of VL and VC are twice that of… | JEE Main 2022 (28 Jun, Shift 2)

Q45JEE Main 2022 · 28 JUN · SHIFT 2Difficult

Series LCR Circuit

In the given circuit, the magnitude of VL and VC are twice that of VR. Given that f = 50 Hz, the inductance of the coil is $\frac{1}{K\pi}$ mH. The value of K is ____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 0

$V_L = V_C$ means $X_L = X_C$ : resonance, so $Z = R = 5\ \Omega$ .
$I = \dfrac{220}{5} = 44\text{ A}$ , $V_R = 220\text{ V}$ , $V_L = 2V_R = 440\text{ V}$ .
$X_L = \dfrac{440}{44} = 10\ \Omega \Rightarrow L = \dfrac{10}{2\pi \times 50} = \dfrac{1}{10\pi}\text{ H} = \dfrac{100}{\pi}\text{ mH}$
$\dfrac{1}{K\pi} = \dfrac{100}{\pi} \Rightarrow K = 0.01$ , which rounds to 0 as an integer answer.

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