Question

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

Answer 1

Correct Answer: 144

Explanation:

$P=I^{2}R$$I_{rms}=\frac{V_{rms}}{Z}$ $(I_{rms}\to$ root mean squaring current$)$$Z=\sqrt{R^2+{(X_L-X_C)}^2}$ $\{z\to$ impidance $\}$$R=R_1+R_2(R\to R_{\text{eq }})$$R=44+36=80\mathrm{\Omega }$$Z=\sqrt{(80{)}^2+(90-60{)}^2}$$=\sqrt{(80{)}^2+(30{)}^2}$$Z=100\mathrm{\Omega }$So, $I_{rms}=\frac{V_{rms}}{Z}=\frac{200\mathrm{\angle }0}{100}=2A$Power deposited in the coil$P=I^2{R}^{}$$P=(2{)}^2\times 36$$P=4\times 36$$P=144$ watt.Hence, the correct answer is 144 watt.