The current through a resistor in an a.c circuit is given as 2 sin wt. Determine the d.c. equivalent of the current
- \(\frac{1A}{\sqrt{2}}\)
-
\(\sqrt{2}\)A
- 2 A
- 2\(\sqrt{2}\)A
The correct answer is: B
Explanation
If I = 2 Sin wt; but in a.c. circuit current I = I\(_0\) Sin wt; thus comparing the two equations, it implies that I\(_0\) = 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) = \(\frac{I_0}{\sqrt{2}}\) = \(\frac{2.0A}{\sqrt{2}}\) = \(\sqrt{2}\)A (by rationalizing the denominator \(\frac{2.0A}{\sqrt{2}}\))
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