In a A-C- circuit- V and I are givne by V -100 sin 100 t volt- I -100 sin100 t -3 A Then the power dissipated in the circuit isA- 104 WB- 10 WC- 2500 WD- 5 W

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RLC Circuit

In a A.C. cir...

Question

In a A.C. circuit, V and I are givne by V = 100 sin(100 t) volt, $I = 100 s i n (100 t + \frac{π}{3}) A$ Then the power dissipated in the circuit is

10^{4}

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10 W

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2500 W

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5 W

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Solution

The correct option is C 2500 W
Considering the given equation for V and I, $E_{0} = 100 V, I_{0} = 100 A$ and $ϕ = \frac{π}{3}$
Then, $E_{r . m . s} = \frac{E_{0}}{\sqrt{2}} = \frac{100}{\sqrt{2}}$ and $I_{r . m . s} = \frac{I_{0}}{\sqrt{2}} = \frac{100}{\sqrt{2}}$
Now, Power dissipated in the circuit is given by $P = E_{r . m . s} I_{r . m . s} c o s ϕ = \frac{100}{\sqrt{2}} \times \frac{100}{\sqrt{2}} \times c o s \frac{π}{3} = \frac{100 \times 100}{2} \times \frac{1}{2} = 2500 W$

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