Match the following

Currents r.m.s. values

(1) X_o sin ωt (i) X_o

(2) X_o sin ω t cos ω t (ii) $\frac{x_{o}}{\sqrt2}$

(3) ${x_0}\sin \omega \,t + {x_0}\cos \omega \,t$ (iii) $\frac{{{x_0}}}{{(2\sqrt 2 )}}$

Moderate

Solution

1. rms value = $\frac{x_{o}}{\sqrt2}$
2. ${x_0}\sin \omega t\cos \omega t = \frac{{{x_0}}}{2}\sin 2\omega t \Rightarrow rms\;\,value = \frac{{{X_0}}}{{2\sqrt 2 }}$
3. ${x_0}\sin \omega t$ $+ {x_0}\cos \omega t \Rightarrow$
$rms\,\,value = \sqrt {(\frac{X_0}{\sqrt{2}})^2+(\frac{X_0}{\sqrt{2}})^2}$
$= \sqrt {x_0^2} = {x_0}$

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