Alternating current and voltage

​​In a nutshell

An alternating current is a type of current which periodically reverses direction. The root mean square values are a type of average used for sinusoidal waveforms.

Equations

Variable definitions

Alternating current

An alternating current (AC) is a type of electric current which periodically reverses direction. It is used in generators, motors and power distributors due to being more efficient than direct current (DC), which is current flowing in only one direction.
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An alternating current follows a waveform such as the one shown below:

1. Current 2. Time

The frequency of the current is the number of times the generators spin per second. The UK mains electricity has a frequency of $$50\ Hz$$.

Root mean square voltage and current

Since alternating current follows a waveform it has peak values. These are the maximum values, regardless of sign, of sinusoidal waves.

• The peak voltage $$V_0$$ is the maximum voltage value, regardless of sign, of an alternating current. 
• The peak current $$I_0$$ is the maximum value, regardless of sign, of an alternating current.
  

To determine the average voltage or current of an alternating current, a simple mean would not work as it will be $$0$$ due to it being a wave. Scientists therefore use the root mean square (r.m.s.) values which are a different type of averaging technique. 

The r.m.s. voltage $$V_{rms}$$​ can be calculated with the formula:

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

The r.m.s. current $$I_{rms}$$​ can be calculated with the formula:

​$$I_{rms}=\dfrac{I_0}{\sqrt{2}}$$​​

Example

The UK mains electricity has a peak voltage of $$\pm325\ V$$, calculate its r.m.s. value.

First, write down what you know:

$$V_0=325\ V$$​​

Next, write down the formula for the r.m.s. voltage:

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$$V_{rms}=\dfrac{V_0}{\sqrt{2}}$$​​

Substitute the values and calculate the r.m.s. voltage:

$$V_{rms}=\dfrac{325}{\sqrt{2}}=230\ V$$​​

The r.m.s. voltage of the UK mains electricity is $$\underline{230\ V}$$.

Oscilloscopes

An oscilloscope is a type of voltmeter where you can manipulate how readings are displayed. You can do this by changing the time-base ($$x-axis$$) and the amplitude ($$y-axis$$). An oscilloscope can be used to obtain information about an alternating current, such as peak values for current and voltage. 

1. Display 2. Time-base dial 3. Amplitude dial