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Question
The line that draws power supply to your house from street has ______.
- zero average current.
- 220 V average voltage.
- voltage and current out of phase by 90°.
- voltage and current possibly differing in phase `phi` such that `|phi| < pi/2`.
Options
b and c
a and d
b and d
a and c
Solution
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.
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