The current through a resistor in an a c circui... - JAMB Physics 2001 Question
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
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Correct Option: B
The given a.c. current is $I(t) = 2 \sin(\omega t)$. The d.c. equivalent of an a.c. current is the root-mean-square (rms) value of the current. The rms value of a sinusoidal current is given by:
$I_{rms} = \frac{I_{peak}}{\sqrt{2}}$
In this case, the peak current, $I_{peak} = 2A$. Therefore,
$I_{rms} = \frac{2}{\sqrt{2}} = \sqrt{2}A$
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