Question 292: AC fundamentals

Question

A $20 \Omega$ resistance, 10 mH inductance coil and $15 \mu \mathrm{~F}$ capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination, the circuit resonates. If the resistance is made $\frac{1}{3} \mathrm{rd}$, the resonant frequency

Accepted Answer

At resonance, $X_L=X_C$
$$ \begin{aligned} & \Rightarrow \quad \omega L=\frac{1}{\omega C} \ & \Rightarrow \quad \omega^2=\frac{1}{\sqrt{L C}} \ & \Rightarrow \quad f=\frac{1}{2 \pi \sqrt{L C}} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(i)\end{aligned} $$
From (i), we can see that the resonant frequency is independent of R .(resistance).
So, if the resistance is made $\left(\frac{1}{3}ight)^{	ext {rd }}$, the resonant frequency remain unchanged.

Answer

remains unchanged.

Answer

is doubled.

Answer

is quadrupled.

Answer

is halved.

AC fundamentals

A 20 \Omega resistance, 10 mH inductance coil and 15 \mu \mathrm{~F} capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination, the circuit resonates. If the resistance is made \frac{1}{3} \mathrm{rd}, the resonant frequency

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