In series LCR resonant circuit; the capacitance is changed from C to 3 C . To obtain the same resonant…
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
$\frac{\mathrm{L}}{3}$
$\frac{\mathrm{L}}{2}$
$\frac{\mathrm{L}}{\sqrt{3}}$
3 L
Solution
At resonance,
$\begin{array}{ll}
& \mathrm{X}_{\mathrm{L}}=\mathrm{X}_{\mathrm{C}} \\
\therefore & \omega \mathrm{~L}=\frac{1}{\omega \mathrm{C}} \\
\therefore & \mathrm{~L} \propto \frac{1}{\mathrm{C}}
\end{array}$
$\therefore \quad$ When C is changed to 3 C , L should be $\frac{\mathrm{L}}{3}$