which one of the following statements concerning an ac circuit is true?

a) when only resistance is present in an ac circuit, voltage and current are in phase.
b) on average, the power dissipated by resistor in an ac circuit is zero.
c) for a resistor in an ac cicuit, the current and voltage are 90 degree out of phase.
d) the current and voltage are in phase for a capacitor in an ac circuit.
e) inductors in an ac circuit offer little opposition to current at high frequencies.

a is true, always.

To determine which statement is true concerning an AC circuit, we'll go through each option and explain how to approach it:

a) When only resistance is present in an AC circuit, voltage and current are in phase.
To check if this statement is true, we need to recall the behavior of a purely resistive circuit. In a purely resistive circuit, the voltage and current waveforms are in phase with each other. This means that they reach their maximum and minimum values at the same time and cross the zero axis (or any given point) together. Therefore, option a) is true.

b) On average, the power dissipated by a resistor in an AC circuit is zero.
To verify this statement, we need to understand that power in an AC circuit can be both positive and negative. However, the negative and positive portions of the power waveform average out to zero over time. Therefore, the average power dissipated by a resistor in an AC circuit is indeed zero. Hence, option b) is true.

c) For a resistor in an AC circuit, the current and voltage are 90 degrees out of phase.
In a purely resistive circuit, such as the one described in option a), the current and voltage are in phase. Therefore, option c) is false.

d) The current and voltage are in phase for a capacitor in an AC circuit.
For a capacitor in an AC circuit, the current and voltage are not in phase. In fact, the current in a capacitor leads the voltage by 90 degrees in an AC circuit. Therefore, option d) is false.

e) Inductors in an AC circuit offer little opposition to current at high frequencies.
This statement is true. At high frequencies in an AC circuit, inductors present more impedance and opposition to the flow of current. In other words, the impedance of an inductor increases with frequency. So, at high frequencies, inductors offer little opposition to the current. Thus, option e) is true.

In conclusion, the statements that are true concerning an AC circuit are:
a) When only resistance is present in an AC circuit, voltage and current are in phase.
b) On average, the power dissipated by a resistor in an AC circuit is zero.
e) Inductors in an AC circuit offer little opposition to current at high frequencies.

The correct statement concerning an AC circuit is:

a) When only resistance is present in an AC circuit, voltage and current are in phase.