Question 68 of 190
When a voltage of is applied to an inductor, a current of flows through it. When an ac voltage of peak value is connected to inductor, its inductive reactance is found to be . The power dissipated in the circuit is _______ W.
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Answer: 250
For DC voltage
for AC voltage
$\begin{aligned}
& \mathrm{X}_{\mathrm{L}}=20 \sqrt{3} \Omega \\
& \mathrm{R}=20 \Omega \\
& \mathrm{Z}=\sqrt{\mathrm{X}_{\mathrm{L}}^2+\mathrm{R}^2}=\sqrt{3 \times 400+400}=40 \Omega \\
& \text { Power }=\mathrm{i}_{\text {rms }}^2 \mathrm{R} \\
& \quad=\left(\frac{\mathrm{V}_{\text {rms }}}{\mathrm{Z}}\right)^2 \times \mathrm{R}=\left(\frac{\frac{200}{\sqrt{2}}}{40}\right)^2 \times 20=250 \mathrm{~W}
\end{aligned}$
for AC voltage
$\begin{aligned}
& \mathrm{X}_{\mathrm{L}}=20 \sqrt{3} \Omega \\
& \mathrm{R}=20 \Omega \\
& \mathrm{Z}=\sqrt{\mathrm{X}_{\mathrm{L}}^2+\mathrm{R}^2}=\sqrt{3 \times 400+400}=40 \Omega \\
& \text { Power }=\mathrm{i}_{\text {rms }}^2 \mathrm{R} \\
& \quad=\left(\frac{\mathrm{V}_{\text {rms }}}{\mathrm{Z}}\right)^2 \times \mathrm{R}=\left(\frac{\frac{200}{\sqrt{2}}}{40}\right)^2 \times 20=250 \mathrm{~W}
\end{aligned}$