Question

Resonant frequency of a LC circuit is 10 kHz. Calculate the value of inductance, if the capacitance is $50\mu F.$

Answer 1

For resonance condition-

$X_L=X_C$

$⟹\omega L=\frac{1}{\omega C}$

$⟹L=\frac{1}{{\omega }^{2}C}$ and

$\omega =2\pi f=20\pi \times {10}^{3}rad/s$

$⟹L=\frac{1}{4\times {\pi }^2\times {10}^8\times 50\times {10}^{-6}}$

$⟹L=5.07\times {10}^{-6}H=5.07\mu H$