# Alternating Currents

A LevelAQA

## Alternating Currents

The mains electricity supply is alternating current (A.C). This section looks at the features of A.C including frequency, root-mean-square current and root-mean-square voltage.

## Alternating Currents

Alternating current (A.C) periodically varies from positive to negative current. If the alternating current supply is plotted against time, a sinusoidal graph is formed showing that the electrons in the wire move back and forth in simple harmonic motion (SHM). The same concept could be used for plotting voltage against time.

The time period can be seen above on the graph and is the time difference between two peak positive currents or two peak negative currents. Frequency of the AC supply can also be calculated as:

$f = \dfrac{1}{T}$

• $f$ is the frequency in Hertz $\left(\text{Hz}\right)$.
• $T$ is the time period in seconds $\left(\text{s}\right)$.

Example: The time period of an AC supply is $0.1 \: \text{s}$. Calculate the frequency of the supply.

[1 mark]

$f = \dfrac{1}{T}$

$f = \dfrac{1}{0.1}$

$f = 10 \: \text{Hz}$

A LevelAQA

## Root-Mean-Square Current

Root-Mean-Square (rms) is used to compare AC and DC (Direct Current) currents. The rms for direct current or voltage represents the value of direct current or voltage that will produce the same power dissipation as alternating current. The rms value is calculated by the square root of the mean of the squares of all values of voltage in one full cycle.

To calculate the rms current $\left(I_{rms}\right)$, the following equation can be used:

$I_{rms} = \dfrac{I_0}{\sqrt{2}}$

where $I_{rms}$ is the rms current and $I_0$ is the peak current. Both are measured in amps $\left(\text{A}\right)$.

To calculate the rms voltage $\left(V_{rms}\right)$, the following equation can be used:

$V_{rms} = \dfrac{V_0}{\sqrt{2}}$

where $V_{rms}$ is the rms voltage and $V_0$ is the peak voltage. Both are measured in volts $\left(\text{V}\right)$.

Example: The peak current read from an oscilloscope trace is $2.5 \: \text{A}$. What is the rms current?

[1 mark]

$I_{rms} = \dfrac{I_0}{\sqrt{2}}$

$I_{rms} = \dfrac{2.5}{\sqrt{2}}$

$I_{rms} = 1.8 \: \text{A}$

A LevelAQA

## Applications of Alternating Current

The UK power supply is an alternating current/voltage. It has a peak voltage of $230 \: \text{V}$ and the frequency of the alternating voltage is $50 \: \text{Hz}$ (switches from positive to negative $50$ times per second). However, this is an average and varies depending upon the time of day, demand and type of consumer.

A LevelAQA

## Alternating Currents Example Questions

The square root of the mean of the squares of all values of voltage in one full cycle.

Gold Standard Education

\begin{aligned} I_{rms} &= \dfrac{I_0}{\sqrt{2}} \\ \\ \boldsymbol{I_{rms}} &= \dfrac{5.25}{\sqrt{2}} = \boldsymbol{3.71} \: \textbf{A} \end{aligned}

Gold Standard Education

Any two from:

• Time of day
• Demand
• Type of consumer

Gold Standard Education

## Alternating Currents Worksheet and Example Questions

### Alternating Current Questions

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