Question:
A $100 \Omega$ resistance, a $0.1 \mu \mathrm{F}$ capacitor and an inductor are connected in series across a $250 \mathrm{~V}$ supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is $60 \mathrm{~Hz}$.
Correct Option: , 4
Solution:
$\mathrm{C}=0.1 \mu \mathrm{F}=10^{-7} \mathrm{~F}$
Resonant frequency = 60 Hz
$\omega_{0}=\frac{1}{\sqrt{L C}}$
$2 \pi \mathrm{f}_{0}=\frac{1}{\sqrt{\mathrm{LC}}} \Rightarrow \mathrm{L}=\frac{1}{4 \pi^{2} \mathrm{f}_{\mathrm{o}}^{2} \mathrm{C}}$
by putting values $L \simeq 70.3 \mathrm{~Hz}$.