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The maximum values of the alternating voltages and current are 400 V and 20 A respectively In a circuit connected to 50 Hz supply and these quantities are sinusoidal. The instantaneous values of the voltage and current are $200 \sqrt{2} V$ and 10 A, respectively. At t = 0, both are increasing positively. Determine the power consumed in the circuit.(in watts)

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answer is 3864.

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Detailed Solution

$ω = 2 π f = (100 π) r a d / s$

From the above two figures, we can write

$V = 400 \sin (ω t + θ_{1}) = 400 \sin [100 π t + \frac{π}{4}] i = 20 \sin (ω t + θ_{2}) = 20 \sin [100 π t + \frac{π}{6}]$

Phase difference between V and i

$ϕ = (π / 4 - π / 6) = \frac{π}{12} o r 15^{0} P = V_{r m s} i_{r m s} \cos ϕ = (\frac{400}{\sqrt{2}}) (\frac{20}{\sqrt{2}}) \cos 15^{0} = 3864 W$

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