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A circuit containing a $80 \mathrm{mH}$ inductor and a $60 \mu \mathrm{F}$ capacitor in series is connected to $230 \mathrm{~V}, 50 \mathrm{~Hz}$ supply. The resistance of the circuit is negligible.
(a) Obtain the current amplitude and rms values.
(b) Obtain the rms values of potential drops across each element.
(c) What is the average power transferred to the inductor?
(d) What is the average power transferred to the capacitor.
(e) What is the total average power absorbed by the circuit? ['Average' implies 'averaged over one cycle".]
(a) Obtain the current amplitude and rms values.
(b) Obtain the rms values of potential drops across each element.
(c) What is the average power transferred to the inductor?
(d) What is the average power transferred to the capacitor.
(e) What is the total average power absorbed by the circuit? ['Average' implies 'averaged over one cycle".]
Solution:
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Verified Answer

(a) Inductive reactance $X_L=2 \pi f L$ $X_L=2 \pi(50) 80 \times 10^{-3}=25.12 \Omega$
Capacitive reactance $X_C=\frac{1}{2 \pi f C}$
$$
X_C=\frac{1}{2 \times 3.14 \times 50 \times 60 \times 10^{-6}}=53.05 \Omega
$$
Impedance $=X_C-X_L=53.05-25.12=27.93 \Omega$
rms value of current $I_v=\frac{E_v}{Z}=\frac{230}{27.93}$
$=8.235 \mathrm{~A}$
Peak Value $I_0=I_{\mathrm{v}} \sqrt{2}=11.644 \mathrm{~A}$
(b) Potential drop across $L, V_L=I_L X_L=206.68 \mathrm{~V}$ Potential drop across $C$, $V_C=I_V \times X_C=436.87 \mathrm{~V}$
(c) Average power transferred to inductor is zero, because of phase difference $\pi / 2$.
$$
\mathrm{P}=E_v I_v \cos \phi . \quad \phi=\pi / 2, \therefore \mathrm{P}=0
$$
(d) Average power transferred to capacitor is also zero, because of phase difference $\pi / 2$.
$$
\begin{aligned}
&\mathrm{P}=E_v I_v \cos \phi . \\
&\phi=\pi / 2, \therefore \mathrm{P}=0
\end{aligned}
$$
(c) Total power absorbed by the circuit
$$
P_{\text {Total }}=P_L+P_C=0
$$
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