Question

A direct current of 5A is superposed on an alternating current I = 10sin ω t flowing through a wire. The effective value of the resulting current will be

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

Hint:

DC and AC components combine using RMS addition, not algebraic sum.

Answer 1

The Correct Option is B

Step 1: RMS value of AC:
\( I_{ac} = \dfrac{10}{\sqrt{2}} = 5\sqrt{2} \)
Step 2: Resultant RMS current:
\( I = \sqrt{I_{dc}^2 + I_{ac}^2} \)
\( = \sqrt{5^2 + (5\sqrt{2})^2} \)
\( I = 5\sqrt{3} \, \text{A} \)