Question:
A direct current of \(5\text{ A}\) is superposed on an alternating current \(I=10\sin\omega t\) flowing through the same wire. The effective value of the resulting current will be:
A direct current of \(5\text{ A}\) is superposed on an alternating current \(I=10\sin\omega t\) flowing through the same wire. The effective value of the resulting current will be:
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DC and AC components combine as:
\[
I_{\text{rms}}=\sqrt{I_{\text{dc}}^2+I_{\text{ac,rms}}^2}
\]
Never add amplitudes directly.
Updated On: Mar 23, 2026
- \(\dfrac{15}{2}\,\text{A}\)
- \(5\sqrt{3}\,\text{A}\)
- \(5\sqrt{5}\,\text{A}\)
- \(15\,\text{A}\)
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The Correct Option is B
Solution and Explanation
Step 1: RMS value of AC component: \[ I_{\text{ac}}=\frac{10}{\sqrt{2}}=5\sqrt{2} \]
Step 2: Total RMS current: \[ I_{\text{rms}}=\sqrt{I_{\text{dc}}^2+I_{\text{ac}}^2} \] \[ =\sqrt{5^2+(5\sqrt{2})^2}=\sqrt{25+50}=5\sqrt{3} \]
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