Question

In a circuit an alternating current and a direct current are supplied together. The expression of the instantaneous current is given as $i = 3 + 6\sin\omega t$. Then the r.m.s. value of the current is

• A. 3A
• B. 6A
• C. $3\sqrt{2}$A
• D. $3\sqrt{3}$A

Answer 1

Answer: (D)

$3\sqrt{3}$A

Answer 2

The given current is a mixture of a dc component of 3A and an alternating current of maximum value 6A

Hence r.m.s. value $= \sqrt{(dc)^{2} + (r.m.s.\text{value of ac})^{2}}$

$= \sqrt{(3)^{2} + \left( \frac{6}{\sqrt{2}} \right)^{2}} = \sqrt{(3)^{2} + (3\sqrt{2})^{2}} = 3\sqrt{3}A$.