Question 335: AC fundamentals

Question

In series LCR resonant circuit, the capacitance is changed from C to 3 C . To obtain the same resonant frequency, the inductance should be changed from $L$ to

Accepted Answer

In a series LCR resonant circuit, the resonant frequency ($f_0$) is given by:
$$ f_0 = \frac{1}{2\pi\sqrt{LC}} $$
where $ L $ is the inductance, and $ C $ is the capacitance.
When the capacitance is increased from $ C $ to $ 3C $, to maintain the same resonant frequency, we need to find the new inductance $ L' $ such that:
$$ f_0 = \frac{1}{2\pi\sqrt{L' \cdot 3C}} $$
Equating the original and adjusted resonant frequencies:
$$ \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi\sqrt{L' \cdot 3C}} $$
Simplifying the equation:
$$ \sqrt{LC} = \sqrt{L' \cdot 3C} $$
Squaring both sides:
$$ LC = L' \cdot 3C $$
Dividing both sides by $ C $:
$$ L = L' \cdot 3 $$
So the new inductance $ L' $ is:
$$ L' = \frac{L}{3} $$
Thus, the correct option is:
Option A: $\frac{L}{3}$

Answer

$\frac{\mathrm{L}}{3}$

Answer

$\frac{\mathrm{L}}{2}$

Answer

$\frac{\mathrm{L}}{\sqrt{3}}$

Answer

$\mathrm{3 L}$

AC fundamentals

In series LCR resonant circuit, the capacitance is changed from C to 3 C . To obtain the same resonant frequency, the inductance should be changed from L to

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