# 7.21 Alternating Currents & Potential Differences

## Alternating Currents & Potential Differences

• An alternating current (a.c) is defined as:

A current which periodically varies between a positive and negative value

• This means the direction of an alternating current switches every half cycle
• The variation of current, or p.d., with time can be described as a sine curve ie. sinusoidal
• Therefore, the electrons in a wire carrying a.c. move back and forth with simple harmonic motion

• As with SHM, the relationship between time period T and frequency  f for a.c is related by the equation:

• Where:
• T = time period (s)
• f = frequency (Hz)

• Peak current (I0), or peak voltage (V0), is defined as:

The maximum value of the alternating current or voltage

• Peak current, or voltage, can be determined from the amplitude of a current-time or voltage-time graph
• The peak-to-peak current or voltage is the distance between a positive and consecutive negative peak. This means:

peak voltage V0 = peak-to-peak voltage ÷ 2

Graph of alternating current against time showing the time period, peak current and peak-to-peak current

#### Root-Mean-Square Current & Voltage

• Root-mean-square (rms) values of current, or voltage, are a useful way of comparing a.c current, or voltage, to its equivalent direct current (d.c), or voltage
• The rms values represent the direct current, or voltage, values that will produce the same heating effect, or power dissipation, as the alternating current, or voltage

• The rms value of an alternating current is defined as:

The equivalent direct current that produces the same power

• In other words, an rms current is 'equivalent', in a sense, to a DC current, because they produce the same overall effect in a circuit

• The rms value of an alternating voltage is similarly defined as:

The equivalent dc voltage that produces the same power

• Rms current is equal to 0.707 × I0, which is about 70% of the peak current I0
• This is also the case for rms voltage

Vrms and peak voltage. The rms voltage is about 70% of the peak voltage

#### Worked example

The variation with time t of the output voltage V of an alternating voltage supply is shown in the graph below.Use the graph to calculate the frequency of the supply and the peak voltage.

#### Exam Tip

Remember to double-check the units on the alternating current and voltage graphs. These are often shown in milliseconds (ms) instead of seconds (s) on the x-axis.

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