Question

in a LCR circuit L=8H,C=0.5 micro Farhad and R=100 ohm. The resonant frequency of the circuit is?

Answer 1

Resonant frequency = 1/ 2pie ×root over LC
= 1/ 2× 3.14 × 8 × 0.5 ×10^-3
= 0.0398× 10^3
= 39.8

Answer 2

$w \: = \sqrt{ \frac{1}{lc} } = \sqrt{ \frac{1}{8 \times 0.5 \times 10^-6} } = \sqrt{ \frac{1}{4 \times 10 ^-6} } = \frac{1}{2 \times 10 ^-3}$
$w = 2 \times f \times \pi \\ = > f = \frac{w}{2\pi} \\ = > f = \frac{1}{2 \times 10 ^ - 3 \times \pi }$
=500\π
= 160 Hz.