Question

If the current and the voltage are out of phase by 90 degree, then the power is; 1) Minimum; 2) Maximum; 3) 1.1 VI; 4) Zero

Answer 1

The power is zero....

Answer 2

The power is zero. hence option (4) is correct.

The current and voltage are out of phase by 90°. then power is ;

1. minimum
2. maximum
3. 1.1VI
4. zero

Instantaneous power :  We know, instantaneous current and voltage are given by i = iₙsinωt and V = Vₙsin(ωt + Φ)

[ Here iₙ and Vₙ indicates average value of current and voltage respectively. ]

We know, Power is the rate of change of energy per unit time.

i.e., P = Vit/t = Vi [ ∵ Energy from Joule's law, E = Vit ]

⇒ P =  [Vₙsin(ωt + Φ)][iₙsinωt]

= (Vₙiₙ/2) [2sinωt sin(ωt + Φ)]

= (Vₙiₙ/2) [cosΦ - cos(2ωt + Φ)] ....(1)

Here We see that the average Power is given by the average of two terms as shown in equation (1). but the power is time independent. so the first term i.e., cosФ is time independent and also its average is zero.

⇒  P = (Vₙiₙ/2)cosΦ = (V₀i₀)cosФ [ where V₀ and i₀ are initial voltage and current respectively. ]

Hence the power of ac circuit is given by P = V₀i₀cosФ

Now, Here you can see that Ф is phase difference of current and voltage.

Ф = 90° [ given ]

P =  (V₀i₀)cos90° = 0

Therefore the power is zero. hence option (4) is correct.

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