Test: Power in an AC Circuit

Explanation: Total voltage= VR+VL+VC.
VR=1000x3x10-3=3V.
Therefore, total voltage = 30+18+3=51V.

Since E and I are in the same phase.
Therefore, phase difference will be 0 and since power factor= cosx (where x= phase difference) and x =0
therefore, cos x or power factor will be =1

P=I_rms V_rms cos ϕ
Where, ϕ=90
cosϕ=0
therefore,P=0
hence the correct answer is option A.

i=2cost
=Im​cost
So, Im​=2amp
IRMS​=Im​​/√​2​
=2/√​2​
=2​amp

The formula of true power is,
True power=Apparent power x power factor
So, true power=10 x 0.5
True power=5W
 

The average power consumed/cycle in an ideal capacitor is 0.
The average power consumed in an ideal capacitor is given as based on the instantaneous power which is supplied to the capacitor:
p_c = iv= (i_m cos ωt)(v_m sin ωt)
p_c = i_mv_m (cos ωt sin ωt)
pc=(i_mv_m/2)sin2ωt
We know that sin ωt = 0
Therefore, average power = 0

Cos x (power factor) = R/Z
= 10/20
=1/2
x= 60

Given that,
Reactance (X) =Resistance (R)
tanϕ = X/R​
So, we have ϕ = π/4​
Power factor = cosϕ = ​1​/√2