An inductor of inductance $2 \mu \mathrm{H}$ is connected in series with a resistance, a variable capacitor…
An inductor of inductance $2 \mu \mathrm{H}$ is connected in series with a resistance, a variable capacitor and an a.c. source of frequency 5 kHz . The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{\mathrm{x}} \mathrm{F}$, where the value of
' $x$ ' is (Take $\pi^2=10$ )
500
1000
2000
4000
Solution
For maximum current to be drawn the circuit should be in resonance,
$\begin{aligned}
& \therefore \quad \mathrm{X}_{\mathrm{L}}=\mathrm{X}_{\mathrm{C}} \quad \Rightarrow 2 \pi \mathrm{fL}=\frac{1}{2 \pi \mathrm{fC}} \\
& \therefore \quad \mathrm{C}=\frac{1}{4 \pi^2 \mathrm{f}^2 \mathrm{~L}}=\frac{1}{4 \times 10 \times 25 \times 10^6 \times 2 \times 10^{-6}} \\
& \therefore \quad \mathrm{C}=\frac{1}{2000} \mathrm{~F} \quad \Rightarrow \mathrm{x}=2000
\end{aligned}$