First slide

Alternating Current and voltage

Question

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

Moderate

A

Zero
B

10 W
C

5 W
D

2.5 W

Solution

$V = 5 cosω t = 5 \sin (ω t + \frac{π}{2})$ and $i = 2 sinω t$
Power $= V_{r . m . s .} \times i_{r . m . s .} \times cosφ$ = 0
(Since $φ = \frac{π}{2}$ , therefore $cosφ = \cos \frac{π}{2} = 0$ )

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