Question

A current is made of two components, a DC component of ${{I}_{1}}=3A$ and an Ac component given by ${{I}_{2}}=4\sin \omega t$, then what is the average value of total current?
A. $3\,A$
B. $4\sqrt{2}\,A$
C. $(3+4\sqrt{2})\,A$
D. $5\,A$

Answer 1

Hint: In direct current, there is unidirectional flow of electric charge. The rate of flow of this unidirectional charge is direct current or DC.
Alternating current is an electric current which reverses its directional periodically. Its magnitude also keeps changing with time. Average AC over a time period is zero.

Complete step by step answer:
The current flowing through the circuit at any time is the sum of both alternating current and direct current at that time. Therefore,
${{I}_{net}}={{I}_{dc}}+{{I}_{ac}}$
${{I}_{net}}=3+4\sin (\omega t)$
When we average the total current over time period of AC current, we get
$\left\langle {{I}_{net}} \right\rangle =3+4\left\langle \sin (\omega t) \right\rangle =3+0=3A$
Since the average of sine function over range ($0,2\pi $) is zero. Therefore, the average alternating current is also zero. The average value of total current is the same as DC current. That is 3 amperes.
Therefore, option A is correct.

Additional information:
The most common waveform in electric power circuits is a sine wave. Alternating current can be produced by using an AC generator or alternator. AC generators work on Faraday’s principle of electromagnetic induction.
AC is the form of current which is mostly used in home appliances. An AC current has a large advantage over DC as it is able to transfer power over large distances without much loss of energy.

Note:
The average of alternating current over its time period is zero. The normal waveforms of AC current in most of the circuits are sinusoidal in which the positive half period corresponds with the positive direction of the current and vice-versa.
The DC current is unidirectional i.e. charge flows in one direction.