JAMB - Physics (2001 - No. 28)
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
Explicació
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 \(\frac{2.0A}{\sqrt{2}}\))
and I(rms) = \(\frac{I_0}{\sqrt{2}}\) = \(\frac{2.0A}{\sqrt{2}}\) = \(\sqrt{2}\)A (by rationalizing the denominator \(\frac{2.0A}{\sqrt{2}}\))