Question

The line that draws power supply to your house from street has ______.

1. zero average current.
2. 220 V average voltage.
3. voltage and current out of phase by 90°.
4. voltage and current possibly differing in phase `phi` such that `|phi| < pi/2`.

विकल्प

• b and c

• a and d

• b and d

• a and c

Answer 1

a and d

Explanation:

Alternating currents are used for household supplies, which are having zero average value over a cycle.

The line is having some resistance, so power factor `cos phi = R/Z ≠ 0`

So, `phi = pi/2 ⇒ phi < pi/2`

i.e., phase lies between 0 and `pi/2`.

Important point: The average value of alternating quantity for one complete cycle is zero.

The average value of ac over half cycle (t = 0 to T/2)

`I_(av) = (int_0^(T/2) i dt)/(int_0^(T/2) dt) = (2i_0)/pi = 0.637i_0` = 63.7% of i₀

Similarly `V_(av) = (2V_0)/pi` = 0.637 V₀ = 63.7% of V₀.