Question

A resistance of $50\Omega$, an inductance of $20\pi \text{H}$ and a capacitor of $\frac{5}{\pi }\mu \text{F}$ are connected in series with an $A.C.$ source of $230\text{volts}$ and $50\text{Hz}$ .The impedance of circuit is_______(in ohm)

Answer 1

Given:
$R=50\Omega ;L=\frac{20}{\pi }\text{H};C=\frac{5}{\pi }\mu \text{F};E=230\text{volts};f=50\text{Hz}$

Inductive reactance, $X_L=\omega L=2\pi \times 50\times \frac{20}{\pi }=2000\Omega$

Capacitive reactance, $X_C=\frac{1}{\omega C}=\frac{1}{2\pi \times 50\times \frac{5}{\pi }\times {10}^{-6}}=2000\Omega$

$\because X_L=X_C$ then $Z=R$

i.e. impedence of circuit $Z=R=50\Omega$