Ncert Exercises & Solutions

The line that draws the power supply to your house from the street has:

(a)	zero average current
(b)	$220~\text V$ average voltage
(c)	voltage and current out of phase by $90^\circ$
(d)	voltage and current possibly differing in phase $\phi$ such that $\|\phi\|<\dfrac \pi 2.$

Choose the correct options:
1. (b), (c)
2. (a), (d)
3. (b), (d)
4. (a), (c)

Hint: AC currents are used in domestic supplies.

Explanation: For household supplies, AC currents are used which have zero average value over a cycle.
The line that draws the power supply to our house from the street supplies alternating current, whose average value/mean value over a cycle is zero. As the line has some resistance,

(R \neq 0),

$(R≠0),$ therefore, voltage and current differ in phase

ϕ

$ϕ$ such that

| ϕ | < π / 2.

$|ϕ|<π/2.$

The line has some resistance so the power factor;

\cos ϕ = \frac{R}{Z} \neq 0

$\cos \phi=\frac{R}{Z} \neq 0$

ϕ \neq π / 2 \Rightarrow ϕ < π / 2

$\phi \neq \pi / 2 \Rightarrow \phi<\pi / 2$
therefore, the phase lies between

0

$0$ and

π / 2.

$\pi/2.$
Hence, option (2) is the correct answer.

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