Discussion
An alternating current I in amperes varies with time t in seconds as I = 4 sin 200πt. The r.m.s. values of the current and frequency are
Answer: B
The values are \(4/\sqrt{2}\) A and 100 Hz.
Comparing \(I = 4\sin 200\pi t\) with \(I = I_0 \sin 2\pi f t\):
\[ \begin{aligned} I_{rms} &= \frac{I_0}{\sqrt{2}} = \frac{4}{\sqrt{2}} = 2.83\ \text{A} \\ 2\pi f &= 200\pi \Rightarrow f = 100\ \text{Hz} \end{aligned} \]
2 A is half the peak, not the r.m.s. value; \(4\sqrt{2}\) A multiplies by root 2 instead of dividing; and 50 Hz comes from taking 200 as \(4\pi f\).
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