Match the following:Currents | vedclass

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(B) The $r.m.s.$ value of a current $I(t)$ is given by $I_{rms} = \sqrt{\frac{1}{T} \int_0^T I^2(t) dt}$.For $(1)$,$I = x_0 \sin \omega t$. The $r.m.s

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$1-(ii), 2-(iii), 3-(i)$

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(B) The $r.m.s.$ value of a current $I(t)$ is given by $I_{rms} = \sqrt{\frac{1}{T} \int_0^T I^2(t) dt}$.For $(1)$,$I = x_0 \sin \omega t$. The $r.m.s.$ value is $\frac{x_0}{\sqrt{2}}$. Thus,$1-(ii)$.For $(2)$,$I = x_0 \sin \omega t \cos \omega t = \frac{x_0}{2} \sin(2\omega t)$. The peak value is $\frac{x_0}{2}$,so the $r.m.s.$ value is $\frac{x_0/2}{\sqrt{2}} = \frac{x_0}{2\sqrt{2}}$. Thus,$2-(iii)$.For $(3)$,$I = x_0 \sin \omega t + x_0 \cos \omega t = \sqrt{2} x_0 \sin(\omega t + \frac{\pi}{4})$. The peak value is $\sqrt{2} x_0$,so the $r.m.s.$ value is $\frac{\sqrt{2} x_0}{\sqrt{2}} = x_0$. Thus,$3-(i)$.Therefore,the correct match is $1-(ii), 2-(iii), 3-(i)$.

Match the following:
Currents $r.m.s.$ values
$(1) x_0 \sin \omega t$ $(i) x_0$
$(2) x_0 \sin \omega t \cos \omega t$ $(ii) \frac{x_0}{\sqrt{2}}$
$(3) x_0 \sin \omega t + x_0 \cos \omega t$ $(iii) \frac{x_0}{2\sqrt{2}}$

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Match the following:Currents $r.m.s.$ values$(1) x_0 \sin \omega t$ $(i) x_0$$(2) x_0 \sin \omega t \cos \omega t$ $(ii) \frac{x_0}{\sqrt{2}}$$(3) x_0 \sin \omega t + x_0 \cos \omega t$ $(iii) \frac{x_0}{2\sqrt{2}}$