Alternating CurrentMedium
Question
The electric current in the circuit is given as $i = i_{o}(t/T)$. The r.m.s current for the period $t = 0$ to $t = T$ is $\_\_\_\_$
Options
A.$\frac{i_{0}}{\sqrt{2}}$
B.$i_{0}$
C.$\frac{i_{0}}{\sqrt{6}}$
D.$\frac{i_{0}}{\sqrt{3}}$
Solution
$i_{rms}^{2} = \frac{\int_{0}^{T}\mspace{2mu}\left( i_{0}^{2}t^{2}/T^{2} \right)dt}{\int_{0}^{T}\mspace{2mu} dt} = \frac{i_{0}^{2}}{{\text{ }T}^{3}} \cdot \frac{{\text{ }T}^{3}}{3} = \frac{i_{0}^{2}}{3}$
$$i_{\text{rms~}} = \frac{i_{0}}{\sqrt{3}}$$
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