Question 218: AC fundamentals

Question

A series LCR circuit with $$R = {{250} \over {11}}\,\Omega $$ and $${X_L} = {{70} \over {11}}\,\Omega $$ is connected across a 220 V, 50 Hz supply. The value of capacitance needed to maximize the average power of the circuit will be _________ $$\mu$$F. (Take : $$\pi  = {{22} \over 7}$$)

Accepted Answer

For maximum power
$$
\begin{aligned}
&	ext { power factor }=\cos 	heta=1\\
& 	herefore \frac{R}{Z}=1 \\
&R^{2}=Z^{2} \\
&R^{2}=\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}ight)^{2}+\mathrm{R}^{2} \\
&\mathrm{X}_{\mathrm{L}}=\mathrm{X}_{\mathrm{C}} \\
&\frac{70}{11}=\frac{1}{100 \pi 	imes C} \\
&\Rightarrow C=\frac{11}{7000 \pi}=500 	imes 10^{-6} F=500 \mu F
\end{aligned}
$$

AC fundamentals

A series LCR circuit with $R = {{250} \over {11}}\,\Omega and {X_L} = {{70} \over {11}}\,\Omega is connected across a 220 V, 50 Hz supply. The value of capacitance needed to maximize the average power of the circuit will be _________ \muF. (Take : \pi = {{22} \over 7}$)

Integer / Numeric Answer Type