Voltage Dividers

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What is a voltage divider?

A voltage divider consists of two resistances R1 and R2 connected in series across a supply voltage Vs. The supply voltage is divided between the two resistances to give an output voltage Vo which is the voltage across R2.

An important use of voltage dividers is to connect input transducers to circuits.

voltage divider circuit

The output voltage Vo depends on the size of R2 relative to R1:

If you need a precise value for the output voltage Vo you can use this formula:

Voltage divider output, Vo =  Vs × R2
 R1 + R2

Important: this formula and the rough rules given above assume that negligible current flows from the output. This is true if Vo is connected to a device with a high resistance such as voltmeter or an IC input. For further information please see the page on impedance. If the output is connected to a transistor Vo cannot become much greater than 0.7V because the transistor's base-emitter junction behaves like a diode.

Potential dividers

Voltage dividers are also known as potential dividers, a name which comes from potential difference (the proper name for voltage).

Using an input transducer (sensor) in a voltage divider

Most input transducers (sensors) vary their resistance and usually a voltage divider is used to convert this to a varying voltage which is more useful. The voltage signal can be fed to other parts of the circuit, such as the input to an IC or a transistor switch.

The sensor is one of the resistances in the voltage divider. It can be at the top (near +Vs) or at the bottom (near 0V), the choice is determined by when you want a large value for the output voltage Vo:

Next you need to choose a value for the resistor (R) which makes up the voltage divider.

Choosing a resistor value

The value of the resistor R determines the range (maximum and minimum values) of the output voltage Vo. For best results you need Vo to have a large range and this is achieved if R is much larger than the sensor's minimum resistance but much smaller than its maximum resistance.

Use a multimeter to find the minimum and maximum values of the sensor's resistance, there is no need to be precise - approximate values will do. Then use the formula to choose a value for resistor R:

R = square root of (Rmin × Rmax)

Rmin = sensor's minimum resistance
Rmax = sensor's maximum resistance

Choose a standard value for R which is close to the calculated value.

For example if your LDR has Rmin = 100ohm and Rmax = 1Mohm: R = square root of (100 × 1M) = 10kohm.

Swapping the resistor and sensor

The resistor and sensor can be swapped over to invert the action of the voltage divider. For example an LDR has a high resistance when dark and a low resistance when brightly lit:

voltage divider with LDR at top

Vo high in bright light

voltage divider with LDR at bottom

Vo high in dark

Using a variable resistor

A variable resistor may be used in place of the fixed resistor R. It will enable you to adjust the output voltage Vo for a given resistance of the sensor. For example you can use a variable resistor to set the exact brightness level which makes an IC change state.

The variable resistor value should be larger than the fixed resistor value it replaces. For finer control you can use a fixed resistor in series with the variable resistor. For example if a 10kohm fixed resistor is suitable you could replace it with a fixed 4.7kohm resistor in series with a 10kohm variable resistor, allowing you to adjust the resistance from 4.7k to 14.7kohm.

Take care using variable resistors with transistors

If you are planning to use a variable resistor connected between the +Vs supply and the base of a transistor you must include a fixed resistor in series with the variable resistor. This is to prevent excessive base current destroying the transistor when the variable resistor is reduced to zero. For further details see the Transistor Circuits page.

voltage divider with variable resistor and LDR

The sensor and variable
resistor can be swapped
over if necessary

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