Question 309: AC fundamentals

Question

A resistor of $50 \Omega$, inductor of self inductance $\left(\frac{3}{\pi^2}\right) \mathrm{H}$ and a capacitor of unknown capacity are connected in series to an a.c. source of 100 V and 50 Hz . When the voltage and current are in phase, the value of capacitance is (nearly)

Accepted Answer

Given: $\mathrm{L}=\frac{3}{\pi^2} \mathrm{H}$ and $\mathrm{f}=50 \mathrm{~Hz}$
As voltage and current are in phase, the circuit is a resonant circuit.
$$\begin{aligned}
	herefore \quad \mathrm{X}_{\mathrm{C}} & =\mathrm{X}_{\mathrm{L}} \
\frac{1}{\omega \mathrm{C}} & =\omega \mathrm{L} \
\mathrm{C}=\frac{1}{\omega^2 \mathrm{~L}} & =\frac{1}{4 \pi^2 \mathrm{f}^2 \mathrm{~L}} \
& =\frac{1}{4 \pi^2 	imes(50)^2 	imes \frac{3}{\pi^2}}=0.33 	imes 10^{-4} \mathrm{~F}
\end{aligned}$$

Answer

$0.66 	imes 10^{-4} \mathrm{~F}$

Answer

$0.33 	imes 10^{-4} \mathrm{~F}$

Answer

$0.66 	imes 10^{-2} \mathrm{~F}$

Answer

$0.33 	imes 10^{-2} \mathrm{~F}$

AC fundamentals

A resistor of 50 \Omega, inductor of self inductance \left(\frac{3}{\pi^2}\right) \mathrm{H} and a capacitor of unknown capacity are connected in series to an a.c. source of 100 V and 50 Hz . When the voltage and current are in phase, the value of capacitance is (nearly)

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