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Chapter 14: Problem 2067

In general in an alternating current circuit. (a) The average value of current is zero. (b) The average value of square of current is zero. (c) Average power dissipation is zero. (d) The phase difference between voltage and current is zero.

Short Answer

Expert verified
In summary, (a) The average value of current is zero, which is correct for AC circuits. (d) The phase difference between voltage and current is zero, which is correct for purely resistive AC circuits but not for general AC circuits with inductors and/or capacitors. However, statements (b) and (c) are incorrect: the average value of square of current is not zero, and the average power dissipation is not zero in an AC circuit.

Step by step solution

01

Statement (a) - Average value of current is zero.

This statement is correct for AC circuits. In an AC circuit, current alternates its direction periodically, and as a result, the average value of the current over a complete cycle is zero. The current waveform is usually sinusoidal, and in one cycle, it has equal positive and negative parts.
02

Statement (b) - The average value of square of current is zero.

This statement is incorrect for AC circuits. The average value of the square of current is not zero. Since squaring a value always gives a positive result, squaring the current will yield a positive value during both the positive and negative halves of the AC cycle, so the average squared current over a cycle will always be greater than zero.
03

Statement (c) - Average power dissipation is zero.

This statement is incorrect for AC circuits. In an AC circuit, the average power dissipation is not zero. While the average voltage and current are zero over a complete cycle, the power dissipation is related to the product of the instantaneous voltage and current, which is not zero in general. In a resistive load, the power follows a quadratic relation, i.e., \(P = VI\), where both voltage and current have equal phase angles. In such a case, the average power will have a positive value.
04

Statement (d) - The phase difference between voltage and current is zero.

This statement is correct when considering purely resistive AC circuits. In a resistive circuit, the voltage and current waveforms are in phase. However, for general AC circuits containing inductors and/or capacitors, the phase difference between voltage and current can be non-zero; such circuits are called reactive circuits.

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Most popular questions from this chapter

In an LCR series ac circuit the voltage across each of the components \(\mathrm{L}, \mathrm{C}\) and \(\mathrm{R}\) is \(50 \mathrm{~V}\). The voltage across the LC combination will be (a) \(50 \mathrm{~V}\) (b) \(50 \sqrt{2} \mathrm{~V}\) (c) \(100 \mathrm{~V}\) (d) \(0 \mathrm{~V}\) (zero)

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