Question 44: AC fundamentals

Question

A series L-C-R circuit is connected to an AC source of 220 V and 50 Hz shown in figure. If the readings of the three voltmeters $$V_1,V_2$$ and $$V_3$$ are 65 V, 415 V and 204 V respectively, the value of inductance and capacitance will be

Accepted Answer

As
$$\begin{aligned}
V & =I_{\mathrm{rms}} R \
I_{\mathrm{rms}} & =\frac{V_R}{R}=\frac{65}{100}=0.65 \mathrm{~A} \
V_L & =I_{\mathrm{rms}} 	imes X_L \
X_L & =\frac{V_L}{I_{\mathrm{rms}}}=\frac{204}{0.65}=313.85 \Omega \
X_L & =\omega L=2 \pi fL\
\mathrm{or} \quad L & =\frac{X_L}{2 \pi f} \
L & =\frac{313.85}{2 	imes \pi 	imes 50}=1.0 \mathrm{H} \
X_C & =\frac{V_C}{I_{\mathrm{rms}}}=\frac{415}{0.65}=638.46 \Omega \
X_C & =\frac{1}{\omega C}=\frac{1}{2 \pi f C} \
C & =\frac{1}{2 	imes \pi 	imes 50 	imes 638.46} \
& =5 	imes 10^{-6}=5 \mu \mathrm{F}
\end{aligned}$$

Answer

2.0 H, 5 $$\mu$$F

Answer

1.0 H, 5 $$\mu$$F

Answer

4.0 H, 6 $$\mu$$F

Answer

1.0 H, 2 $$\mu$$F

AC fundamentals

A series L-C-R circuit is connected to an AC source of 220 V and 50 Hz shown in figure. If the readings of the three voltmeters $V_1,V_2 and V_3$ are 65 V, 415 V and 204 V respectively, the value of inductance and capacitance will be

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