In an a.c. circuit, voltage and current are given by: V = 100 sin ( 100 t ) V and I = 100 sin 100 t + π 3 mA respectively. The average power dissipated in one cycle is :

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TestHub · Accepted Answer

Standard expression of voltage is given by, $V = V_{0} \sin (ω t)$ and for current is given by, $I = I_{0} \sin (ω t + ϕ)$ . Clearly, $ϕ$ is the phase difference here. From the given expression, $ϕ = \frac{π}{3}$ .

Average power dissipated in one cycle is given by,

$P_{a v g} = V_{r m s} I_{r m s} \cos (ϕ)$

$= \frac{100}{\sqrt{2}} \times \frac{100 \times 10^{- 3}}{\sqrt{2}} \times \cos (\frac{π}{3})$

$= \frac{10^{4}}{2} \times 10^{- 3} \times \frac{1}{2}$

$= \frac{10}{4} = 2.5 W$

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