Question

A $100\Omega$ resistance, a $0.1\mu F$ capacitor and an inductor are connected in series across a $250\text{V}$ supply at variable frequency. Calculate the value of inductance of inductor at which resonance will ocur. Given that the resonant frequency is $60\text{Hz}$

• A. $0.70\text{H}$
• B. $70.4\text{mH}$
• C. $7.03\times {10}^{-5}\text{H}$
• D. $70.4\text{H}$

Answer 1

The correct option is D $70.4\text{H}$

Given, $C=0.1\mu F={10}^{-7}F$
Resonant frequency $=60\text{Hz}$
We know that, at resonance
${\omega }_0=\frac{1}{\sqrt{LC}}$
$\Rightarrow 2\pi f_0=\frac{1}{\sqrt{LC}}\Rightarrow L=\frac{1}{4{\pi }^2{f}_0^{2}C}$
by putting values
$L=\frac{1}{4\times (3.14{)}^2\times {60}^2\times {10}^{-7}}=\frac{{10}^7}{4\times (3.14{)}^2\times 3600}\Rightarrow L=70.43\text{H}$
Thus, option (d) is correct.