The rms value of the emf given by E = (8 sin | vedclass

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

Question

(A) The given emf is $E = 8 \sin \omega t + 6 \cos \omega t$. We can express this in the form $E = A \sin(\omega t + \phi)$,where $A$ is the peak ampl

Vedclass · Accepted Answer

$5 \sqrt{2} 	ext{ V}$

Vedclass · Answer

(A) The given emf is $E = 8 \sin \omega t + 6 \cos \omega t$. We can express this in the form $E = A \sin(\omega t + \phi)$,where $A$ is the peak amplitude. Comparing $8 \sin \omega t + 6 \cos \omega t$ with $A \sin(\omega t + \phi) = A \sin \omega t \cos \phi + A \cos \omega t \sin \phi$,we get: $A \cos \phi = 8$ and $A \sin \phi = 6$. Squaring and adding these equations: $A^2(\cos^2 \phi + \sin^2 \phi) = 8^2 + 6^2$ $A^2 = 64 + 36 = 100$ $A = 10 	ext{ V}$. The rms value $E_{rms}$ is related to the peak value $A$ by the formula $E_{rms} = \frac{A}{\sqrt{2}}$. $E_{rms} = \frac{10}{\sqrt{2}} = \frac{10 	imes \sqrt{2}}{2} = 5 \sqrt{2} 	ext{ V}$.

The rms value of the emf given by $E = (8 \sin \omega t + 6 \cos \omega t) \text{ V}$ is:

Similar Questions

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

The $ rms $ value of current in a $ 50 \,Hz $ $ AC $ circuit is $ 6 \,A $. The average value of $ AC $ current over a complete cycle is:

An $AC$ source is rated $222 \,V, 60 \,Hz$. The average voltage is calculated in a time interval of $16.67 \,ms$. It

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

$A$ resistance of $20 \Omega$ is connected to a source of an alternating potential $V = 200 \sin (10 \pi t)$. If $t$ is the time taken by the current to change from the peak value to rms value,then $t$ is (in seconds).

Vedclass Test Series

Exam Paper Generator

Online Exam Module