When a voltage vs=200√2sin(ω t + 15 ° ) is applied to an AC circuit, the current in the circuit is found to be i=2sin(ω t + π / 4) then average power consumed in the circuit is

Question

When a voltage vs=200√2sin(ω t + 15 ° ) is applied to an AC circuit, the current in the circuit is found to be i=2sin(ω t + π / 4) then average power consumed in the circuit is (A) 200 watt (B) 400√2 watt (C) 100√6 watt (D) 200√2 watt

Tardigrade Admin · Accepted Answer

Correction 150 arrow 15° Pav=vrmsIrmscosÏ =(200 √2/√2)(2/√2)⋅ cos(30 ° )=200√2cos(15) =200√2[(1/√2) ((√3/2) + (1/2))] =200[(√3 + 1/2)]=100(√3 + 1)

Q. When a voltage $v_{s} = 2002 s in (ω t + 1 5^{\circ})$ is applied to an AC circuit, the current in the circuit is found to be $i = 2 s in (ω t + π /4)$ then average power consumed in the circuit is

$200$ watt

$4002$ watt

$1006$ watt

$2002$ watt

Correction $150 \to 1 5^{\circ}$
$P_{a v} = v_{r m s} I_{r m s} cos ϕ$
$= \frac{200 2}{2} \frac{2}{2} \cdot cos (3 0^{\circ}) = 2002 cos (15)$
$= 2002 [\frac{1}{2} (\frac{3}{2} + \frac{1}{2})]$
$= 200 [\frac{3 + 1}{2}] = 100 (3 + 1)$

Q. When a voltage vs​=2002​sin(ωt+15∘) is applied to an AC circuit, the current in the circuit is found to be i=2sin(ωt+π/4) then average power consumed in the circuit is

200 watt

4002​ watt

1006​ watt

2002​ watt