Q129 / 180 · COMEDK 2012 · Physics
An inductor and a resistor are connected to an $\mathrm{AC}$ supply of $50 \mathrm{~V}$ and $50 \mathrm{~Hz}$. If the voltage across the resistor is $40 \mathrm{~V}$, then the voltage across the inductor will be
- A$10 \mathrm{~V}$
- B$20 \mathrm{~V}$
- Correct answerC$30 \mathrm{~V}$
- D$60 \mathrm{~V}$
Solution
Given, $V_{S}=50 \mathrm{~V}, V_{R}=40 \mathrm{~V}$
For an $L-R$ circuit,
$$
\begin{aligned}
V_{S} &=\sqrt{V_{R}^{2}+V_{L}^{2}} \\
\Rightarrow \quad V_{L} &=\sqrt{V_{S}^{2}-V_{R}^{2}} \\
&=\sqrt{50^{2}-40^{2}} \\
&=\sqrt{2500-1600}=\sqrt{900}=30 \mathrm{~V}
\end{aligned}
$$
Hence, the correct answer is option: 'C'.