In a circuit,current varies with time as i = | vedclass

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

Question

(B) The root mean square $(RMS)$ current is defined as $I_{rms} = \sqrt{\frac{1}{T_2 - T_1} \int_{T_1}^{T_2} i^2 dt}$.Given $i = 2\sqrt{t}$,so $i^2 =

Vedclass · Accepted Answer

$2\sqrt{3}\,A$

Vedclass · Answer

(B) The root mean square $(RMS)$ current is defined as $I_{rms} = \sqrt{\frac{1}{T_2 - T_1} \int_{T_1}^{T_2} i^2 dt}$.Given $i = 2\sqrt{t}$,so $i^2 = 4t$.The time interval is from $T_1 = 2\,s$ to $T_2 = 4\,s$,so $T_2 - T_1 = 4 - 2 = 2\,s$.Now,calculate the integral: $\int_{2}^{4} 4t \,dt = [2t^2]_{2}^{4} = 2(4^2 - 2^2) = 2(16 - 4) = 2(12) = 24$.Substitute these values into the $RMS$ formula:$I_{rms} = \sqrt{\frac{24}{2}} = \sqrt{12} = \sqrt{4 	imes 3} = 2\sqrt{3}\,A$.

In a circuit,current varies with time as $i = 2\sqrt{t}$. The root mean square value of current for the interval $t = 2\,s$ to $t = 4\,s$ is:

Similar Questions

If an $AC$ main supply is given to be $220 \ V$,what would be the average e.m.f. during a positive half cycle?

$A$ group of lamps having a total power rating of $1000 \,W$ is supplied by an $AC$ voltage of $E = 200 \sin(310t + 60^{\circ})$. The $r.m.s.$ value of the current flowing through the circuit is:

If an $AC$ main supply is given to be $220\,V$,the average $emf$ during a positive half cycle will be.....$V$.

In an $AC$ generator, induced emf $\varepsilon = 0$ at $t = 0$, then its value . . . . . .

An alternating e.m.f. is given by $e = e_0 \sin \omega t$. In how much time will the e.m.f. have half its maximum value,if $e$ starts from zero? $(T = \text{time period}, \sin 30^{\circ} = 1/2)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module