Answer to Question #315051 in Electric Circuits for Apc

Question

In an R-L-C series circuit a maximum current of 0.5 A is obtained by varying the value of inductance L. The supply voltage is fixed at 230 V, 50 Hz. When maximum current flows through the circuit, the voltage measured across the capacitor is 350 V. What are the values of the cricuit parameters? 15

Answer 1

We know that

$Z=\sqrt{R^2+(X_L-X_C)^2}$

Maximum current

$X_L=X_c$

Now impedance

$Z=R$

$i_{max}=\frac{V}{R}$

$R=\frac{230}{0.5}=460\Omega$

Now capacitor across Voltage

$V=X_L I$

$V=w LI$

$L=\frac{V}{2\pi f I}$

$L=\frac{230}{2\times3.14\times50\times0.5}=1.464H$

Critical condition

$X_L=X_c\\wL=\frac{1}{wC}$

$C=\frac{1}{w^2L}$

$C=\frac{1}{(2\times3.14\times50)^2\times 1.464}=6.92\times10^{-6}F$

$C=6.92\mu F$