A resistance of 20 Omega is connected to an a | vedclass

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

Question

(D) The instantaneous current in an $A.C.$ circuit is given by $i = i_0 \sin(\omega t + \phi)$.At maximum value,$i = i_0$,which occurs at $\omega t_1

Vedclass · Accepted Answer

$2.5 ms$

Vedclass · Answer

(D) The instantaneous current in an $A.C.$ circuit is given by $i = i_0 \sin(\omega t + \phi)$.At maximum value,$i = i_0$,which occurs at $\omega t_1 = \frac{\pi}{2}$.At $R.M.S.$ value,$i = i_{R.M.S.} = \frac{i_0}{\sqrt{2}}$,which occurs at $\omega t_2 = \frac{\pi}{4}$ (or $\frac{3\pi}{4}$).The time interval $\Delta t = t_1 - t_2$ is given by $\omega \Delta t = \frac{\pi}{2} - \frac{\pi}{4} = \frac{\pi}{4}$.Since $\omega = 2 \pi f$,we have $2 \pi f \Delta t = \frac{\pi}{4}$.Substituting $f = 50 Hz$,we get $2 \pi (50) \Delta t = \frac{\pi}{4}$.$100 \pi \Delta t = \frac{\pi}{4} \Rightarrow \Delta t = \frac{1}{400} s$.$\Delta t = 0.0025 s = 2.5 ms$.

$A$ resistance of $20 \Omega$ is connected to an alternating current source of $110 V$. If the frequency of the $A.C.$ source is $50 Hz$,then the time taken by the current to change from its maximum value to the $R.M.S.$ value is

Similar Questions

An alternating current is given by the equation $i = i_{1} \sin \omega t + i_{2} \cos \omega t$. The rms current will be

What is the approximate percentage value of the ratio of maximum voltage to its rms value in an $LCR$ $AC$ circuit (in $\%$)?

Find the time required for a $50 \text{ Hz}$ alternating current to reach its $rms$ value from zero. (in $\text{ ms}$)

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

In a certain circuit,the current changes with time according to $i = 2\sqrt{t}$. The r.m.s. value of the current between $t = 2 \ s$ and $t = 4 \ s$ will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module