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 $r.m.s.$ voltage of the waveform shown is......$V$

The peak voltage of the $ac$ source is equal to:

The direct current which would give the same heating effect in an equal constant resistance as the current shown in the figure,i.e.,the $r.m.s.$ current,is.....$A$

The instantaneous values of current and voltage in an $AC$ circuit are given by $I = 6 \sin(100 \pi t + \frac{\pi}{4})$ and $V = 5 \sin(100 \pi t - \frac{\pi}{4})$. Then,

The average value of the potential difference $V$ shown in the figure is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module