In an a.c. circuit, voltage and current are given by : $V=100 \sin (100 t)$ V and $I=100 \sin \left(100 t+\frac{\pi}{3}\right)$ mA respectively. The average power dissipated in one cycle is :

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Alternating Current

In an a.c. circuit, voltage and current are given by :

V = 100 sin (100 t)

V and

I = 100 sin (100 t + \frac{π}{3})

mA respectively.
The average power dissipated in one cycle is :

Answer: (C)

Average power dissipated in an AC circuit is

P_{a v g} = V_{r m s} I_{r m s} cos ϕ

, where

ϕ

is the phase difference between voltage and current.

Here

V_{0} = 100

I_{0} = 100

= 0.1

A, and

ϕ = \frac{π}{3}

V_{r m s} = \frac{100}{2}, I_{r m s} = \frac{0.1}{2}

P_{a v g} = \frac{100}{2} \times \frac{0.1}{2} \times cos \frac{π}{3} = \frac{10}{2} \times \frac{1}{2} = 2.5 W

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Single correct option