In an AC circuit the instantaneous values of emf and current are e=200 sin 300 t volt and i=2 sin (300 t+(π/3)) a m p the average power consumed in watts is

Question

In an AC circuit the instantaneous values of emf and current are e=200 sin 300 t volt and i=2 sin (300 t+(π/3)) a m p the average power consumed in watts is (A) 200 (B) 100 (C) 50 (D) 400

Tardigrade Admin · Accepted Answer

The average power consumed in an AC circuit is given by

P = \frac{V _{0} I _{0}}{2} cos ϕ

where

ϕ

is phase angle and

V_{0}

and

I_{0}

the peak value of voltage and current.
Given,

V_{0} = 200 V, I_{0} = 2 A, ϕ = \frac{π}{3}

.

P = \frac{200 \times 2}{2} cos \frac{π}{3}

= \frac{200 \times 2}{2} \times \frac{1}{2} = 100 W

Q. In an AC circuit the instantaneous values of emf and current are e=200sin300t volt and i=2sin(300t+3π​)amp the average power consumed in watts is

200

100

50

400

The average power consumed in an AC circuit is given by P=2V0​I0​​cosϕ where ϕ is phase angle and V0​ and I0​ the peak value of voltage and current. Given, V0​=200V,I0​=2A,ϕ=3π​. P=2200×2​cos3π​ =2200×2​×21​=100W

Q. In an AC circuit the instantaneous values of emf and current are $e = 200 sin 300 t$ volt and $i = 2 sin (300 t + \frac{π}{3}) am p$ the average power consumed in watts is