Question

An oscillating circuit contains an inductor of inductance ${10}^{-6}$ H and two capacitor each of capacitance $5\times {10}^{-6}$ farad connected in parallel. Then the resonance frequency of the circuit is

• A. $\frac{{10}^5}{2\pi }$
• B. $\frac{{10}^5}{\pi }$
• C. $\frac{{3\times 10}^5}{2\pi }$
• D. $\frac{\sqrt{{2\times 10}^5}}{\pi }$

Answer 1

The correct option is C $\frac{{3\times 10}^5}{2\pi }$

$\omega =\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{{10}^{-6}\times 2\times 5\times {10}^{-6}}}$
$=\sqrt{{10}^{11}}\approx 3\times {10}^5$
$f=\frac{\omega }{2\pi }=\frac{3\times {10}^5}{2\pi }$
$=\frac{{1.5\times 10}^5}{\pi }$