# Alternating Currents: Definition, Examples, Symbol (2023)

An alternating current (AC) is a current that periodically varies its magnitude over time in a sinusoidal waveform. The main characteristic of alternating current is the alternating magnitude between positive and negative values.

Modern power generating stations produce electricity in the form of alternating currents. Alternating current is distributed in residential and commercial areas, and it is the main form of electrical power we use in all our electrical appliances.

## How is alternating current produced?

Alternating currents are produced by an AC generator, which consists of a wire that rotates in a magnetic field created by magnets. As the wire rotates in the magnetic field, it cuts through the magnetic flux lines. The changing magnetic flux through the wire generates a force (electromotive force) that drives the electric charges around the wire. The circulating conducting wire creates an oscillating electric current flowing in two directions depending on the varying polarity of the magnet. An elementary generator (AC electrical generator that creates a single, continuously alternating voltage)

Check out our explanation on Emf and Internal Resistance for more info on the electromotive force.

## The alternating current graph

Because alternating currents move periodically and sinusoidally, their motion can be represented by the sine graph. The alternating current graph (which you can see below) expresses the relation between voltage and time.

The AC alternates its intensity with respect to time, alternating between positive and negative values. This means that when alternating current flows through a circuit, the current will flow through the components in both directions. An AC will reach maximum and minimum values in terms of magnitude and will then oscillate between them (±Imax), repeating this cycle every time period T.

### The direct current graph

A graph illustrating the motion of direct current (DC) is shown below. The direct current has a constant magnitude over time (in other words, it is not oscillating).

In the graph, you can see the alternating current in green (sine graph) and the direct current in red (line graph). Graph of alternating current and direct current

## The alternating current equation

We can express AC mathematically as a sine wave equation, as shown below. Imax is the maximum value of current in amperes (A), I is the current at any given time, ω is the supply angular frequency in radians per second (rad/s), and t is time in seconds (s).

$I = I_{max} \cdot \sin(\omega t)$

Similarly, we can use the same equation to express voltage over time, where V is the voltage at any given time in volts (V), and Vmax is the maximum voltage.

$V = V_{max} \cdot \sin(\omega t)$

The period can also be expressed in terms of frequency or angular velocity when convenient. Here, f is the frequency in Herz (Hz), and $$\omega$$ is the angular velocity (rad/s).

$T = \frac{1}{f} = \frac{2 \pi }{\omega}$

The oscillating period between negative and positive is around 50-60Hz depending on the country. In the UK specifically, the AC has a frequency of 50Hz.

## The differences between direct current and alternating current

There are many differences between alternating current and direct current. Alternating current oscillates in two directions, whereas direct current has a constant magnitude over time. This is due to the mechanism that generates AC, which is a rotating coil between two magnets.

In AC, as the coil rotates, the direction of the electrons flowing through the coil changes depending on its position with respect to the poles. This is due to the slip rings connected to the coil. However, in the production of DC, split rings connected to the coil change the contacts between the coil and the circuit wires, which results in the current flowing in one direction only.

Furthermore, the frequency of DC is zero, whereas the frequency for AC supplied to our homes is between 50 and 60Hz. Also, since the current alternates directions in AC, it is described by a sinusoidal motion (hence the voltage varies). In DC, the voltage and current are both constant.

The table below lists the major differences between alternating current and direct current.

 Alternating Current (AC) Direct Current (DC) Oscillates in two directions. Has positive and negative magnitudes. Magnitude is constant over time. Has a peak value of current. The current is constant over time. Electrons in the carrying wire move in two directions. The continuous flow of electrons is in one direction. The current-time graph is sinusoidal. The current-time graph is linear with a constant value. Can be transmitted over long distances. Cannot be transmitted over long distances. AC generators use slip rings and brushes. DC generators use a split-ring commutator.

### Applications of alternating current and direct current

Alternating current is used to power some electrical motors, for example, AC induction motors. AC is also used to transmit electrical energy from power generation stations to urban areas for commercial and personal use and other industrial use facilities. AC is used to transmit electrical energy from power stations to urban areas

Direct current is used mainly in low-voltage applications, such as different battery cells found in smartphone batteries, laptop batteries, or car batteries. DC is also used in solar panels, where the DC is then converted into AC for daily usage.

## Root-mean-square current and voltage

Root mean square (RMS) voltage and root mean square current compare alternating currents to direct currents. We use RMS values for AC, which is the equivalent of the DC value that produces the same amount of work. Multimeters, alternating current voltmeters, and ammeters give a reading of the RMS values of the AC values. Below are the equations to find RMS current and RMS voltage:

$I_{RMS} = \frac{I_{max}}{\sqrt{2}}; \space V_{RMS} = \frac{V_{max}}{\sqrt{2}}$

The graph below represents a voltage-time AC graph (in this case, the symbol V is represented by u, but you must always use V for voltage!). The number 3 represents the RMS voltage. Sinusoidal voltage. 1 represents the amplitude (peak), two is the peak-to-peak, 3 is the RMS, and 4 is the wave period.

### Alternating current examples (with RMS)

Alternating current occurs in many household appliances like fans, internet routers, and motors. This is why it's important to be able to get to grips with the key quantities and calculations involved with alternating currents.

Find the AC RMS values of a current that produces a maximum voltage of 250V and a maximum current of 5A.

Solution

We use the equations given for AC RMS values and plug in the maximum voltage and current values.

\begin{align} I_{RMS} = \frac{I_{max}}{\sqrt{2}} = \frac{5A}{\sqrt{2}} = 3.54 A \\ \space V_{RMS} = \frac{V_{max}}{\sqrt{2}} = \frac{250 V}{\sqrt{2}} = 176.8 V \end{align}

Find the AC maximum voltage and current value based on the AC RMS values of 150V and 2.15A.

Solution

We use the equations given for AC RMS values, rearrange solving for Imax and Vmax, and plug in the RMS voltage and current values.

$I_{RMS} = \frac{I_{max}}{\sqrt{2}} \Rightarrow I_{max} = I_{RMS} \cdot \sqrt 2 = 2.15 A \cdot \sqrt 2 = 3.04 A$

$V_{RMS} = \frac{V_{max}}{\sqrt 2} \Rightarrow V_{max} = V_{RMS} \cdot \sqrt 2 = 150 V\sqrt 2 = 212.1 V$

## Alternating Currents - Key takeaways

• Alternating current (AC) is an oscillating current flowing in two directions with an alternating magnitude.

• Alternating current is distributed in residential and commercial areas, and it is the main form of electrical power we use in all our electrical appliances.

• Alternating currents are produced by an AC generator, which consists of a wire that rotates in a magnetic field created by magnets.

• Alternating currents move periodically and sinusoidally, so the sine graph can represent their motion.

• There are many differences between alternating current and direct current (DC). AC oscillates in two directions, whereas DC has a constant magnitude over time.

• Root mean square (RMS) voltage and root mean square current compare alternating currents to direct currents.

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