Question 261: AC fundamentals

Question

A resistor of $5 . \Omega$, inductor of self inductance $\left(\frac{2}{\pi^2}\right) \mathrm{H}$ and a capacitor of unknown capacity are connected in series to an a.c. source of $100 \mathrm{~V}, 50 \mathrm{~Hz}$ supply. When the voltage and current are in phase, the value of capacitance is

Accepted Answer

Given: $L=\frac{2}{\pi^2} H$ and $f=50 \mathrm{~Hz}$
As voltage and current are in phase, the circuit is a resonant circuit.
$$ \begin{aligned} 	herefore \quad & X_C=X_L \ & \frac{1}{\omega C}=\omega L \end{aligned} $$
$$ \begin{aligned} C & =\frac{1}{\omega^2 L}=\frac{1}{4 \pi^2 f^2 L} \ & =\frac{1}{4 \pi^2 	imes(50)^2 	imes \frac{2}{\pi^2}}=50 	imes 10^{-6} \mathrm{~F}=50 \mu \mathrm{~F} \end{aligned} $$

Answer

$10 \mu \mathrm{~F}$

Answer

$20 \mu \mathrm{~F}$

Answer

$40 \mu \mathrm{~F}$

Answer

$50 \mu \mathrm{~F}$

AC fundamentals

A resistor of 5 . \Omega, inductor of self inductance \left(\frac{2}{\pi^2}\right) \mathrm{H} and a capacitor of unknown capacity are connected in series to an a.c. source of 100 \mathrm{~V}, 50 \mathrm{~Hz} supply. When the voltage and current are in phase, the value of capacitance is

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