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

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Q. As given in the figure, a series circuit connected across $200\, V,\, 60\, Hz$ 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 the coil isPhysics Question Image

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Solution:

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Impedance of the circuit, $Z=\sqrt{\left(R_{1}+R_{2}\right)^{2}+\left(X_{L}-X_{C}\right)^{2}}$
$=\sqrt{(44+36)^{2}+(90-30)^{2}}=\sqrt{(80)^{2}+(60)^{2}}=100 \Omega$
Current in the circuit, $I=\frac{V}{Z}=\frac{200 V }{100 \Omega}=2\, A$
Power dissipated in the coil $=I^{2} R_{2}=(2 A )^{2}(36 \Omega)=144\, W$