Question

A $100 \,\Omega$ resistance, a $0.1\, \mu F$ 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 $60\, Hz$.

• A. $0.70 \,H$
• B. $70.3 \,mH$
• C. $7.03 \times 10^{-5} \,H$
• D. $70.3\,H$

Answer 1

Answer: (D)

$C=0.1 \,\mu F=10^{-7} F$
Resonant frequency $=60 \,Hz$
$\omega_{o}=\frac{1}{\sqrt{L C}} $
$2 \pi f_{0}=\frac{1}{\sqrt{L C}}$
$ \Rightarrow L=\frac{1}{4 \pi^{2} f_{0}^{2} C}$
by putting values $L \simeq 70.3 \,Hz$