Question

In a series $LCR$ circuit $L=10mH$, $C=1$ $\mu F$ and $R=3$$\Omega$. It is connected to an AC voltage source. The inductive reactance of the circuit at a frequency $25$% less than resonant frequency is

• A. $75\Omega$
• B. $100\Omega$
• C. $125\Omega$
• D. $150\Omega$

Answer 1

The correct option is A $75\Omega$

Resonant frequency ${\omega }_r=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{10\times {10}^{-3}\times {10}^{-6}}}=\frac{1}{{10}^{-4}}rad/s$

Given, frequency = $75$% of ${\omega }_r$
$\omega =\frac{3}{4}{\omega }_r=\frac{3}{4\times {10}^{-4}}rad/s$

$\therefore$ Inductive reactance $X_L=\omega L=\frac{3}{4\times {10}^{-4}}\times 10\times {10}^{-3}=75\Omega$