Question

A circuit is set up by connecting inductance L=100mH resistor R=100$\Omega$ and a capacitor of reactance 200$\Omega$ in series An alternating emf of 150$\sqrt{2}V,500m^{-1}$ Hz is applied across this series combination. Calculate the power dissipated.

Answer 1

Given the r.m.s value of emf in the circuit $E_v=150\sqrt{2}V$

The impedance of the LCR circuit is given by

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

$Z=\sqrt{R^2+(2\pi fL-200{)}^2}$

$Z=\sqrt{{100}^2+(2\pi \times \frac{500}{\pi }\times L-200{)}^2}$

$Z=100\sqrt{2}\Omega$

The r.m.s value of current $I_v$ in the circuit is given by

$I_V=\frac{E_V}{Z}=\frac{150\sqrt{2}}{100\sqrt{2}}=1.5A$

Power dissipated in the resistor $=E_V{I}_V=318.2W$