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Question: The potential difference V and the current i flowing through an instrument in an ac circuit of frequ...

The potential difference V and the current i flowing through an instrument in an ac circuit of frequency f are given by V=5cosωtV = 5 \cos \omega t volts and I = 2 sin ωt amperes (where ω = 2πf). The power dissipated in the instrument is

A

Zero

B

10 W

C

5 W

D

2.5 W

Answer

Zero

Explanation

Solution

V=5cosωt=5sin(ωt+π2)V = 5 \cos \omega t = 5 \sin \left( \omega t + \frac { \pi } { 2 } \right) and i=2sinωti = 2 \sin \omega t

Power =Vr.m.s. ×ir.m.s. ×cosϕ= V _ { \text {r.m.s. } } \times i _ { \text {r.m.s. } } \times \cos \phi = 0

(Since ϕ=π2\phi = \frac { \pi } { 2 }, therefore cosϕ=cosπ2=0\cos \phi = \cos \frac { \pi } { 2 } = 0 )