Question

In an L-C-R series resonant circuit, the angular frequency at resonance is ‘ω’. When the inductance of inductance is made twice and capacitance of the capacitor is made four times, the angular frequency at resonance is ‘ω₁’. The ratio of ω: ω₁ is

Options

• 2: 1

• 2√2: 1

• 1: √2

• 1: √2

Answer 1

2√2: 1

Explanation:

Resonant frequency \[\omega=\frac{1}{\sqrt{\mathrm{LC}}}\]

\[\omega_1=\frac{1}{\sqrt{2\mathrm{L}\times4\mathrm{C}}}=\frac{1}{\sqrt{8\mathrm{LC}}}\]

\[=\frac{1}{\sqrt{8}}\cdot\omega=\frac{1}{2\sqrt{2}}\omega\]

\[\frac{\omega}{\omega_1}=\frac{2\sqrt{2}}{1}\]