In an AC circuit, the instantaneous values of emf and current are e=200sin 314 t volt and I=sin (314 t + (π /3)) A . The average power consumed in watt is

Question

In an AC circuit, the instantaneous values of emf and current are e=200sin 314 t volt and I=sin (314 t + (π /3)) A . The average power consumed in watt is (A) 200 (B) 100 (C) 50 (D) 25

Tardigrade Admin · Accepted Answer

Vr m s=(200/√2), Ir m s=(1/√2) ∴ P=Vr m sIr m scos φ =(200/√2)(1/√2)cos â¡ (π /3)=50 W

Q. In an AC circuit, the instantaneous values of emf and current are $e = 200 s in 314 t$ volt and $I = s in (314 t + \frac{π}{3})$ A $.$ The average power consumed in watt is

200

100

50

25

$V_{r m s} = \frac{200}{2}, I_{r m s} = \frac{1}{2}$
$∴ P = V_{r m s} I_{r m s} cos ϕ = \frac{200}{2} \frac{1}{2} cos \frac{π}{3} = 50 W$

Q. In an AC circuit, the instantaneous values of emf and current are e=200sin314t volt and I=sin(314t+3π​) A . The average power consumed in watt is

200

100

50

25

Vrms​=2​200​,Irms​=2​1​ ∴P=Vrms​Irms​cosϕ=2​200​2​1​cos⁡3π​=50W

Q. In an AC circuit, the instantaneous values of emf and current are $e = 200 s in 314 t$ volt and $I = s in (314 t + \frac{π}{3})$ A $.$ The average power consumed in watt is

$V_{r m s} = \frac{200}{2}, I_{r m s} = \frac{1}{2}$
$∴ P = V_{r m s} I_{r m s} cos ϕ = \frac{200}{2} \frac{1}{2} cos \frac{π}{3} = 50 W$