In an A.C. circuit,the e.m.f. (varepsilon) an | vedclass

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

Question

(B) The instantaneous power $p$ in an $A.C.$ circuit is given by the product of instantaneous $e.m.f.$ and instantaneous current:$p = E \cdot i = (E_o

Vedclass · Accepted Answer

$P = \frac{E_o I_o}{2} \cos \phi$

Vedclass · Answer

(B) The instantaneous power $p$ in an $A.C.$ circuit is given by the product of instantaneous $e.m.f.$ and instantaneous current:$p = E \cdot i = (E_o \sin \omega t) \cdot (I_o \sin(\omega t - \phi))$Using the trigonometric identity $\sin A \sin B = \frac{1}{2} [\cos(A-B) - \cos(A+B)]$,we get:$p = \frac{E_o I_o}{2} [\cos \phi - \cos(2\omega t - \phi)]$The average power $P_{av}$ over one complete cycle $T$ is the average of the instantaneous power:$P_{av} = \frac{1}{T} \int_0^T p \, dt = \frac{1}{T} \int_0^T \frac{E_o I_o}{2} [\cos \phi - \cos(2\omega t - \phi)] \, dt$Since the average of $\cos(2\omega t - \phi)$ over a complete cycle is $0$,we have:$P_{av} = \frac{E_o I_o}{2} \cos \phi$Thus,the average power is $\frac{E_o I_o}{2} \cos \phi$.

In an $A.C.$ circuit,the $e.m.f.$ $(\varepsilon)$ and the current $(i)$ at any instant are given respectively by $E = E_o \sin \omega t$ and $i = I_o \sin(\omega t - \phi)$. The average power in the circuit over one cycle of $A.C.$ is:

Similar Questions

In an $ac$ circuit,$V$ and $I$ are given by $V = 100 \sin(100t) \text{ V}$ and $I = 100 \sin(100t + \frac{\pi}{3}) \text{ mA}$. The power dissipated in the circuit is ....... $W$.

When a voltage $V_{s} = 200 \sqrt{2} \sin(\omega t + 15^{\circ})$ is applied to an $AC$ circuit,the current in the circuit is found to be $I = 2 \sin(\omega t + 45^{\circ})$. The average power consumed in the circuit is:

The $r.m.s.$ current in an $ac$ circuit is $2 \ A$. If the wattless current is $\sqrt{3} \ A$,the power factor is:

The power factor of an $AC$ circuit containing peak current $2 \ A$ and peak voltage $1 \ V$ is $1/2$. The angle between voltage and current is: (in $^{\circ}$)

In an $ac$ circuit,the power factor

Vedclass Test Series

Exam Paper Generator

Online Exam Module