Alternating Current Question 8

Question 8 - 29 January - Shift 2

An inductor of inductance $2 \mu H$ is connected in series with a resistance, a variable capacitor and an $AC$ source of frequency $7 kHz$. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x} F$, where the value of $x$ is

(Take $\pi=\frac{22}{7}$ )

Show Answer

Answer: (3872)

Solution:

Formula: Resonant Frequency

$\frac{1}{2 \pi fC}=2 \pi fL$

$C=\frac{1}{4 \pi^{2} f^{2} L}=\frac{1}{4 \times \pi^{2} \times 49 \times 10^{6} \times 2 \times 10^{-6}}$

$C=\frac{1}{3872} F$

$x=3872$