Question

In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 µF and resistance R is 100Ω. The frequency at which resonance occurs is ______.

Options

• 15.9 kHz

• 1.59 rad/s

• 1.59 kHz

• 15.9 rad/s

Answer 1

In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 µF and resistance R is 100Ω. The frequency at which resonance occurs is 1.59 kHz.

Explanation:

In resonance condition of the LCR circuit.

X_L = X_c

⇒ \[\omega_{r}L=\frac{1}{\omega_{r}C}\]

ω_r = \[\frac {1}{\sqrt {LC}}\]

\[f_r=\frac{1}{2\pi\sqrt{LC}}\]

= \[\frac{1}{2\pi\sqrt{10\times10^{-3}\times10^{-6}}}\]

= 1.59 kHz. (where symbols have their usual meanings.)