Question 255: AC fundamentals

Question

In an LC circuit, angular frequency at resonance is $\omega$. The new angular frequency when inductance is made four times and capacitance is made eight times is

Accepted Answer

An LC circuit has angular frequency at resonance as
$ \omega = \frac{1}{\sqrt{LC}}. $
Step 1: Write initial expression
$ \omega = \frac{1}{\sqrt{LC}} $
Step 2: Apply changes
New inductance: $L' = 4L$
New capacitance: $C' = 8C$
New angular frequency:
$ \omega' = \frac{1}{\sqrt{L' C'}} = \frac{1}{\sqrt{(4L)(8C)}} . $
Step 3: Simplify
$ \omega' = \frac{1}{\sqrt{32 LC}}. $
Factor relation to original:
$ \omega = \frac{1}{\sqrt{LC}}. $
So
$ \omega' = \frac{1}{\sqrt{32}} \cdot \frac{1}{\sqrt{LC}} = \frac{\omega}{\sqrt{32}}. $
Step 4: Simplify further
$ \sqrt{32} = \sqrt{16 \cdot 2} = 4 \sqrt{2}. $
So
$ \omega' = \frac{\omega}{4\sqrt{2}}. $
Final Answer:
Option B: $	frac{\omega}{4\sqrt{2}}$
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Answer

$\frac{\omega}{2 \sqrt{2}}$

Answer

$\frac{\omega}{4 \sqrt{2}}$

Answer

$\frac{\omega}{4}$

Answer

$\frac{\omega}{\sqrt{2}}$

AC fundamentals

In an LC circuit, angular frequency at resonance is \omega. The new angular frequency when inductance is made four times and capacitance is made eight times is

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