The current through a resistor in an A.C circuit is given as 2 sin wt. Determine the D.C. equivalent of the current?

A. A/√2
B. 2/√A
C. 2 A
D. √2 A

Correct Answer:

Option B = 2/√A

Explanation

If I = 2 Sin wt; but in a.c. circuit current I = I₀ Sin wt; thus comparing the two equations, it implies that I₀ = 2A; Again, the root means square (I_(rms)) of an a.c. current is the value of the d.c. current that will dissipate the same amount of heat in a given resistance as the a.c.
and I_(rms) = I₀/√2 = 2.0A/√2