# 3.1 Voltage dividers

Voltage dividers are widely used in electronic circuits to create a reference voltage, or to reduce the amplitude of a signal. Figure 12 shows a voltage divider. The value of can be calculated from the values of , and .

Figure 12 A voltage divider circuit

In the first instance, let’s assume that is not connected to anything (for voltage dividers it is always assumed that negligible current flows through ). This means that, according to Kirchhoff’s first law, the current flowing through is the same as the current flowing through . Ohm’s law allows you to calculate the current through . It is the potential difference across that resistor, divided by its resistance. Since the voltage is distributed over two resistors, the potential drop over is .

The current through () is given by

Similarly, the current through is given by

Kirchoff’s first law tells you that , and therefore

Multiplying both sides by and by gives

Then multiplying out the brackets on the right-hand side gives

This can be rearranged to

giving

and therefore the fundamental result is obtained:

## SAQ 3

Suppose = 24 V and = 100 Ω. You want = 6 V. What value of do you need?

### Answer

Rearranging the equation for gives

and therefore

which means the equation for is

Substituting in the values given,

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