1. Why Power in a circuit is Zero (0), in which Current and Voltage are 90 Degree out of phase?

             If Current and Voltage are 90 Degree Out of Phase, Then The Power (P) will be zero. The reason is that, 

We know that Power in AC Circuit 

P= V I Cos φ

if angle between current and Voltage are 90 ( φ = 90) Degree. then

Power P = V I Cos ( 90) = 0

[ Note that Cos (90) = 0] 

So if you put Cos 90 = 0→Then Power will be Zero (In pure Inductive circuit)

2. Why Power in pure Inductive Circuit is Zero (0).

                 We know that in Pure inductive circuit, current is lagging by 90 degree from voltage ( in other words, Voltage is leading 90 Degree from current) i.e the pahse difference between current and voltage is 90 degree. 

So If Current and Voltage are 90 Degree Out of Phase, Then The Power (P) will be zero. The reason is that,

We know that Power in AC Circuit

P= V I Cos φ

if angle between current and Voltage are 90 ( φ = 90) Degree. then

Power P = V I Cos ( 90) = 0

[ Note that Cos (90) = 0]So if you put Cos 90 = 0→Then Power will be Zero (In pure Inductive circuit)

3. Why Power in pure Capacitive Circuit is Zero (0)?

            We know that in Pure capacitive circuit, current is leading by 90 degree from voltage ( in other words, Voltage is lagging 90 Degree from current) i.e the phase difference between current and voltage is 90 degree.

So If Current and Voltage are 90 Degree Out of Phase, Then The Power (P) will be zero. The reason is that,

We know that Power in AC Circuit

P= V I Cos φ

if angle between current and Voltage are 90 ( φ = 90) Degree. then

Power P = V I Cos ( 90) = 0

[ Note that Cos (90) = 0]So if you put Cos 90 = 0→Then Power will be Zero (In pure capacitive circuit)