Q93 / 110 · VITEEE 2023 · Physics
What direct current will produce the same amount of thermal energy in a resistance \(R=\) \(2 \Omega\) as an alternating current that a peak value of \(4.24 \mathrm{~A}\) and frequency \(50 \mathrm{~Hz}\) ?
- Correct answerA\(3 \mathrm{~A}\)
- B\(2 \mathrm{~A}\)
- C\(5 \mathrm{~A}\)
- D\(4 \mathrm{~A}\)
Solution
Peak current, \(\mathrm{I}_0=4.24 \mathrm{~A}\)
\(\mathrm{I}_{\mathrm{rms}}=\frac{\mathrm{I}_0}{\sqrt{2}}=\left(\frac{4.24}{\sqrt{2}}\right)\)
Thermal energy produced,
\(\begin{aligned}
& \mathrm{H}=\mathrm{I}_{\mathrm{d}}^2 \mathrm{RT}=\mathrm{I}_{\mathrm{rms}}^2 \mathrm{RT} \\
& \mathrm{I}_{\mathrm{d}}=\sqrt{\mathrm{I}_{\mathrm{rms}}^2}
\end{aligned}\)
Direct current,
\(I_d=\sqrt{\left(\frac{4.24}{\sqrt{2}}\right)^2}=\frac{4.24}{\sqrt{2}}=2.99 \mathrm{~A} \simeq 3 \mathrm{~A}\)
Hence, the correct answer is option: 'A'.