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A device ' $\mathrm{X}$ ' is connected to an $\mathrm{AC}$ source. The variation of voltage, current and power in one complete cycle is shown in figure.
(a) Which curve shows power consumption over a full cycle?
(b) What is the average power consumption over a cycle?
(c) Identify the device $\mathrm{X}$.
(a) Which curve shows power consumption over a full cycle?
(b) What is the average power consumption over a cycle?
(c) Identify the device $\mathrm{X}$.
Solution:
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Verified Answer
(a) As we know that,
$$
\text { Power }=\mathrm{P}=\mathrm{VI}
$$
The curve of power will be having maximum amplitude, equals to multiplication of amplitudes of voltage $(\mathrm{V})$ and current (I) curve. So, the curve will be represented by A. It shows the power consumption over a cycle, the power of a circuit will become zero, when $V=0$ or $\mathrm{I}=0$ or both become zero, which is clear from graph 'A' is zero at this position.
(b) In the shown by shaded area in the diagram, the full cycle of the graph consists of one positive and one negative symmetrical area are equal. So net area of power graph is zero. So, power consumption in circuit
is zero.
So, that average power of $\mathrm{AC}$ circuit over a cycle is zero.
(c) As the average power is zero, hence the device may be inductor (L) or capacitor (C) or the series combination of L and C. So power factor $\cos \phi=0,(\phi=$ $\left.90^{\circ}\right)$
$$
\text { Power }=\mathrm{P}=\mathrm{VI}
$$
The curve of power will be having maximum amplitude, equals to multiplication of amplitudes of voltage $(\mathrm{V})$ and current (I) curve. So, the curve will be represented by A. It shows the power consumption over a cycle, the power of a circuit will become zero, when $V=0$ or $\mathrm{I}=0$ or both become zero, which is clear from graph 'A' is zero at this position.
(b) In the shown by shaded area in the diagram, the full cycle of the graph consists of one positive and one negative symmetrical area are equal. So net area of power graph is zero. So, power consumption in circuit
is zero.
So, that average power of $\mathrm{AC}$ circuit over a cycle is zero.
(c) As the average power is zero, hence the device may be inductor (L) or capacitor (C) or the series combination of L and C. So power factor $\cos \phi=0,(\phi=$ $\left.90^{\circ}\right)$
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