Question

As given in the figure, a series circuit connected across a 200 V, 60 Hz line consists of a capacitor of capacitive reactance $30\Omega$, a non-inductive resistor of $44\Omega$, and a coil of inductive reactance $90\Omega$ and resistance $36\Omega$ . The power dissipated (in Watt) in the coil is

Answer 1

Given,

$V_{rms}=200V,f=60Hz$

$X_c=30,R_1=44$

$X_L=90,R_2=36$

$\therefore$ Total resistance,

$R=R_1+R_2=44+36=80$

Impedance,

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

$\Rightarrow Z=\sqrt{(80{)}^2+(90-30{)}^2}$

$\Rightarrow Z=\sqrt{(80{)}^2+(60{)}^2}$

$\Rightarrow Z=100$

rms current,

$\Rightarrow I_{rms}=\frac{V_{rms}}{Z}=\frac{200V}{100}=2A$

Power dissipated in the coil

$P_d=I_{rms}^2{R}_2$

(Power is dissipated only in resistor part)

$\Rightarrow P_d=(2{)}^2\times 36$

$\Rightarrow P_d=144W$

Hence, power dissipated in the coil is 144 W.