Question 338: AC fundamentals

Question

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 $\pi^2=10$)

Accepted Answer

For maximum current to be drawn the circuit should be in resonance,
$$\begin{array}{ll}
	herefore & \mathrm{X}_{\mathrm{L}}=\mathrm{X}_{\mathrm{C}} \Rightarrow 2 \pi \mathrm{fL}=\frac{1}{2 \pi \mathrm{C}} \
	herefore & \mathrm{C}=\frac{1}{4 \pi^2 \mathrm{f}^2 \mathrm{~L}}=\frac{1}{4 	imes 10 	imes 25 	imes 10^6 	imes 2 	imes 10^{-6}} \
	herefore & \mathrm{C}=\frac{1}{2000} \mathrm{~F} \quad \Rightarrow \mathrm{x}=2000
\end{array}$$

Answer

500

Answer

1000

Answer

2000

Answer

4000

AC fundamentals

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