First slide

Alternating current and voltage

Question

In a certain circuit current changes with time according to $i = 2 \sqrt{t} .$ r.m.s. value of current between t=1 to t=4s will be

Difficult

A

3 A
B

$\sqrt{10} A$
C

$2 \sqrt{3} A$
D

$(2 - \sqrt{2}) A$

Solution

$\begin{array}{l} \bar{i^{2}} = \frac{\int_{}^{} i^{2} d t}{\int_{}^{} d t} = \frac{\int_{1}^{4} (4 t) d t}{\int_{1}^{4} d t} = \frac{4 \int_{1}^{4} t d t}{3} = \frac{4}{3} {[\frac{t^{2}}{2}]}_{1}^{4} = \frac{2}{3} {[t^{2}]}_{1}^{4} = \frac{2}{3} \times 15 = 10 \\ \Rightarrow i_{r m s} = \sqrt{\bar{i^{2}}} = \sqrt{10} A \end{array}$

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