Question

In a series LCR circuit L = 10 mH, 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 $\omega =\frac{3}{4}{\omega }_r=\frac{3}{4\times {10}^{-4}}rad/s$

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