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, \((R≠0),\) therefore, voltage and current differ in phase \(ϕ\) such that \(|ϕ|<π/2. \)

The line has some resistance so the power factor;
\( \cos \phi=\frac{R}{Z} \neq 0 \)
\(\phi \neq \pi / 2 \Rightarrow \phi<\pi / 2\)
therefore, the phase lies between \(0\) and \(\pi/2.\)
Hence, option (2) is the correct answer.

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