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. \(\dfrac{15}{2}\,\text{A}\)
• B. \(5\sqrt{3}\,\text{A}\)
• C. \(5\sqrt{5}\,\text{A}\)
• D. \(15\,\text{A}\)

Hint:

DC and AC components combine as: \[ I_{\text{rms}}=\sqrt{I_{\text{dc}}^2+I_{\text{ac,rms}}^2} \] Never add amplitudes directly.

Answer 1

The Correct Option is B

Step 1: RMS value of AC component: \[ I_{\text{ac}}=\frac{10}{\sqrt{2}}=5\sqrt{2} \]
Step 2: Total RMS current: \[ I_{\text{rms}}=\sqrt{I_{\text{dc}}^2+I_{\text{ac}}^2} \] \[ =\sqrt{5^2+(5\sqrt{2})^2}=\sqrt{25+50}=5\sqrt{3} \]