Question

In L-C-R series resonant circuit, angular frequency at resonance is '\(\omega\)'. When the inductance of inductor is made twice and capacitance of the capacitor is made four times, the angular frequency at resonance is '\(\omega_1\)'. The ratio of \(\omega:\omega_1\) is

• A. 2 : 1
• B. \(2\sqrt{2}\) : 1
• C. 1 : \(\sqrt{2}\)
• D. 1 : 2

Hint:

Use \(\omega=1/\sqrt{LC}\) for both circuits.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
At resonance in a series LCR circuit, \(\omega=\dfrac{1}{\sqrt{LC}}\).

Step 2: New circuit
With \(L'=2L\) and \(C'=4C\): \(\omega_1=\dfrac{1}{\sqrt{8LC}}\).

Step 3: Ratio
\(\dfrac{\omega}{\omega_1}=\sqrt{8}=2\sqrt{2}\).

Final Answer:
The ratio of the two angular frequencies is \(2\sqrt{2}:1\). \[ \boxed{\text{(B) }2\sqrt{2} : 1} \]