Q68 / 90 · JEE Main 2021 (27 Jul Shift 2) · Physics

A $100 Ω$ resistance, a $0.1 μ F$ capacitor and an inductor are connected in series across a $250 V$ supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is $60 Hz$ .

Solution

$C = 0.1 μ F = 10^{- 7} F$

Resonant frequency $= 60 Hz$

$ω_{o} = \frac{1}{\sqrt{LC}}$

$2 π f_{0} = \frac{1}{\sqrt{L C}} \Rightarrow L = \frac{1}{4 π^{2} f_{0}^{2} C}$

by putting values $L ≃ 70.3 Hz$ .

Hence, the correct answer is option: 'D'.