In an ac circuit,the instantaneous voltage e( | vedclass

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

Question

(D) Given voltage $e(t) = 5[\cos \omega t + \sqrt{3} \sin \omega t]$.Multiplying and dividing by $2$,we get $e(t) = 10[\frac{1}{2} \cos \omega t + \fr

Vedclass · Accepted Answer

Current leads voltage by $\frac{\pi}{12}$

Vedclass · Answer

(D) Given voltage $e(t) = 5[\cos \omega t + \sqrt{3} \sin \omega t]$.Multiplying and dividing by $2$,we get $e(t) = 10[\frac{1}{2} \cos \omega t + \frac{\sqrt{3}}{2} \sin \omega t]$.Using the identity $\sin(A+B) = \sin A \cos B + \cos A \sin B$,we can write $e(t) = 10 \sin(\omega t + \frac{\pi}{3})$.The current is given as $i(t) = 5 \sin(\omega t + \frac{\pi}{4})$.The phase of voltage is $\phi_v = \frac{\pi}{3}$ and the phase of current is $\phi_i = \frac{\pi}{4}$.The phase difference is $\Delta \phi = \phi_v - \phi_i = \frac{\pi}{3} - \frac{\pi}{4} = \frac{4\pi - 3\pi}{12} = \frac{\pi}{12}$.Since $\phi_v > \phi_i$,the voltage leads the current by $\frac{\pi}{12}$. However,checking the options,the current leads the voltage by $-\frac{\pi}{12}$ or voltage leads current by $\frac{\pi}{12}$. Given the standard interpretation of such problems,if the current leads by $\frac{\pi}{12}$ is not an option,we re-evaluate: $\phi_i - \phi_v = \frac{\pi}{4} - \frac{\pi}{3} = -\frac{\pi}{12}$. Thus,voltage leads current by $\frac{\pi}{12}$. Since this is not listed,let's re-check the calculation: $\frac{\pi}{3} \approx 60^\circ$,$\frac{\pi}{4} = 45^\circ$. $60^\circ - 45^\circ = 15^\circ = \frac{\pi}{12}$. The correct physical result is voltage leads current by $\frac{\pi}{12}$. Given the provided options,there might be a typo in the question's options,but based on the math,the phase difference is $\frac{\pi}{12}$.

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.

Similar Questions

The average value of alternating current $I = I_0 \sin \omega t$ in the time interval $[0, \frac{\pi}{\omega}]$ is:

$A$ 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

$AC$ measuring instruments measure

Voltage and current in an $ac$ circuit are given by $V = 5\sin(100\pi t - \frac{\pi}{6})$ and $I = 4\sin(100\pi t + \frac{\pi}{6})$. Which of the following statements is correct?

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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module