Test: Power in an AC Circuit - JEE MCQ

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.

Explanation:

Power in an AC circuit is equal to Instantaneous voltage X Instantaneous current:

- In an AC circuit, both voltage and current vary with time, and power is the rate at which work is done or energy is transferred.
- Power in an AC circuit is given by the product of the instantaneous voltage and the instantaneous current at any given moment.
- This means that at any instant, the power being dissipated or consumed in the circuit can be calculated by multiplying the instantaneous voltage and current values at that particular moment.
- Mathematically, the formula for power in an AC circuit is P = V(t) * I(t), where P is power, V(t) is the instantaneous voltage, and I(t) is the instantaneous current at a given time t.
- Therefore, the correct answer is A: Instantaneous voltage X Instantaneous current.

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