Question

A sinusodial voltage of peak value 283 V and frequency 50 Hz i applied across a LCR circuit in which $R=3\Omega$ $L=25.48mH$ $C=796\mu F$. Find the impedance of the circuit.

Answer 1

$v=283vf=50Hz$

$\omega =2\pi f=2\times \pi \times 50$

$\omega =10pirad/s$

$R=3\Omega L=25.48m/sC=796\mu F$

$X_L=\omega L$

$=100\times \pi \times 25.48\times {10}^{-3}$

$X_L=8\Omega$

$X_c=\frac{1}{\omega c}=\frac{1}{100\pi \times 796\times {10}^{-6}}=$

$X_c=4\Omega$

Now $100$perdance $z=\sqrt{R^2+(X_L-X_C{)}^2}$

$z=\sqrt{3^2+(8-4)}=\sqrt{3^2+4^2}$

$z=5\Omega$