A current in a circuit is given by i = 3 + 4 | vedclass

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

Question

(C) The given current is $i = 3 + 4 \sin \omega t$.To find the $RMS$ value,we first calculate the mean square value $i^2_{rms} = \overline{i^2}$.$i^2

Vedclass · Accepted Answer

$\sqrt{17}$

Vedclass · Answer

(C) The given current is $i = 3 + 4 \sin \omega t$.To find the $RMS$ value,we first calculate the mean square value $i^2_{rms} = \overline{i^2}$.$i^2 = (3 + 4 \sin \omega t)^2 = 9 + 16 \sin^2 \omega t + 24 \sin \omega t$.Taking the average over a full cycle:$\overline{i^2} = \overline{9} + 16 \overline{\sin^2 \omega t} + 24 \overline{\sin \omega t}$.We know that $\overline{\sin^2 \omega t} = 1/2$ and $\overline{\sin \omega t} = 0$ over a full cycle.Therefore,$i^2_{rms} = 9 + 16(1/2) + 0 = 9 + 8 = 17$.The $RMS$ value is $i_{rms} = \sqrt{\overline{i^2}} = \sqrt{17}$.

$A$ current in a circuit is given by $i = 3 + 4 \sin \omega t$. Then the effective value ($RMS$ value) of the current is:

Similar Questions

The peak value of $220 \, V$ of $ac$ mains is ...... $V$.

What is the $r.m.s.$ value of an alternating current which,when passed through a resistor,produces heat that is thrice the heat produced by a direct current of $2 \ A$ in the same resistor (in $A$)?

Both alternating current and direct current are measured in amperes. But how is the ampere defined for an alternating current?

The alternating current in a circuit is described by the graph shown in the figure. Calculate the root mean square $(I_{rms})$ current for this waveform.

An $AC$ current is given by $I = I_{1} \sin \omega t + I_{2} \cos \omega t$. $A$ hot wire ammeter will give a reading of:

Vedclass Test Series

Exam Paper Generator

Online Exam Module