Question 63 of 190

A capacitor of reactance $4 \sqrt{3} \Omega$ and a resistor of resistance $4 \Omega$ are connected in series with an ac source of peak value $8 \sqrt{2} \mathrm{~V}$. The power dissipation in the circuit is ________ W.

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Answer: 4

$\begin{aligned} & \mathrm{Z}=\sqrt{\mathrm{R}^2+\mathrm{X}^2 \mathrm{~L}} \\ & \mathrm{Z}=\sqrt{4^2+(4 \sqrt{3})^2}=8 \Omega \\ & \mathrm{V}_{\mathrm{rms}}=\frac{\mathrm{V}}{\sqrt{2}}=\frac{8 \sqrt{2}}{\sqrt{2}}=(8 \mathrm{~V}) \\ & \mathrm{I}_{\mathrm{rms}}=\frac{\mathrm{V}_{\mathrm{rms}}}{\mathrm{Z}}=\frac{8}{8}=1 \mathrm{~A}\end{aligned}$
Power dissipated $=\mathrm{I}_{\mathrm{rms}}^2 \times \mathrm{R}=1 \times 4=(4 \mathrm{~W})$