In an ac circuit,the r.m.s. value of current, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The $r.m.s.$ (root mean square) value of an alternating current is defined as the square root of the mean of the squares of the instantaneous curr

Vedclass · Accepted Answer

$I_{rms} = \frac{1}{\sqrt{2}} I_0$

Vedclass · Answer

(B) The $r.m.s.$ (root mean square) value of an alternating current is defined as the square root of the mean of the squares of the instantaneous currents over one complete cycle.For a sinusoidal alternating current given by $I = I_0 \sin(\omega t)$,the $r.m.s.$ value is calculated as:$I_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} I^2 dt} = \sqrt{\frac{1}{T} \int_{0}^{T} I_0^2 \sin^2(\omega t) dt}$Solving this integral over one period $T$ gives:$I_{rms} = \frac{I_0}{\sqrt{2}}$Therefore,the correct relation is $I_{rms} = \frac{1}{\sqrt{2}} I_0$.

In an $ac$ circuit,the $r.m.s.$ value of current,$I_{rms}$ is related to the peak current,$I_0$ by the relation:

Similar Questions

The current in an $AC$ circuit is given by $i = i_1 \sin \omega t + i_2 \cos \omega t$. Its $r.m.s.$ value is:

In an $ac$ circuit,the instantaneous voltage $e(t)$ and current $i(t)$ are given by $e(t) = 5[\cos \omega t + \sqrt{3} \sin \omega t] \ V$ and $i(t) = 5[\sin(\omega t + \frac{\pi}{4})] \ A$. Determine the phase relationship between voltage and current.

The voltage of domestic $AC$ is $220\,V$. What does this represent?

In a circuit,the value of the alternating current is measured by a hot wire ammeter as $10 \ A$. Its peak value will be: (in $A$)

The r.m.s. voltage of domestic electricity supply is $220 \ V$. Electrical appliances should be designed to withstand an instantaneous voltage of......$V$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module