Question

As given in the figure, a series circuit connected across a $200\text{V}$, $60\text{Hz}$ 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 the coil is


​​​​​​​$[$1 Mark$]$

• A. $320\text{W}$
• B. $176\text{W}$
• C. $144\text{W}$
• D. $0\text{W}$

Answer 1

The correct option is C $144\text{W}$


Impedance of the circuit, $Z=\sqrt{(R_1+R_2{)}^2+(X_L-X_C{)}^2}$

$Z=\sqrt{(44+36{)}^2+(90-30{)}^2}=\sqrt{(80{)}^2+(60{)}^2}=100\Omega$

Current in the circuit, $I=\frac{V}{Z}=\frac{200\text{V}}{100\Omega }=2\text{A}$

Power dissipated in the coil $P=I^2{R}_2=(2{)}^2\times (36)=144\text{W}$