4.5.1 Potential Divider Circuits

Potential Divider Circuit

• When two resistors are connected in series, through Kirchhoff’s Second Law, the potential difference across the power source is divided between them
• Potential dividers are circuits that produce an output voltage as a fraction of its input voltage
• This is done by using two resistors in series to split or divide the voltage of the supply in a chosen ratio
• Potential dividers have two main purposes:
• To provide a variable potential difference
• To enable a specific potential difference to be chosen
• To split the potential difference of a power source between two or more components
• Potential dividers are used widely in volume controls and sensory circuits using LDRs and thermistors

The Potentiometer

• A potentiometer is similar to a variable resistor connected as a potential divider to give a continuously variable output voltage
• It can be used as a means of comparing potential differences in different parts of the circuit
• The circuit symbol is recognised by an arrow next to the resistor

Potentiometer circuit diagram

• A potentiometer is a single component that (in its simplest form) consists of a coil of wire with a sliding contact, midway along it

A potentiometer is a type of variable resistor

• It is recognised on a circuit diagram with a resistor fitted with a sliding contact
• The sliding contact has the effect of separating the potentiometer into two parts (an upper part and a lower part), both of which have different resistances

Moving the slider (the arrow in the diagram) changes the resistance (and hence potential difference) of the upper and lower parts of the potentiometer

• If the slider in the above diagram is moved upwards, the resistance of the lower part will increase and so the potential difference across it will also increase
• Therefore, the variable resistor obtains a maximum or minimum value for the output voltage
• If the resistance is 3 Ω:
• Maximum voltage is when the resistance is 3 Ω
• Minimum voltage is when the resistance is 0 Ω

Potential Divider Equations

• Since potential divider circuits are based on the ratio of voltage between components, this is equal to the ratio of the resistances of the resistors
• This is shown in the diagram and equation below:

Potential divider diagram and equation

• The input voltage Vin is applied to the top and bottom of the series resistors
• The output voltage Vout is measured from the centre to the bottom of resistor R2
• The potential difference V across each resistor depends upon its resistance R:
• The resistor with the largest resistance will have a greater potential difference than the other one from V = IR
• If the resistance of one of the resistors is increased, it will get a greater share of the potential difference, whilst the other resistor will get a smaller share
• In potential divider circuits, the p.d across a component is proportional to its resistance from V = IR
• Another potential divider equation is one written as a ratio of the potential difference and resistances:

• Where:
• V1 = potential difference of R1 (V)
• V2 = potential difference or R2 (V)
• Using Ohm’s Law, these can also be written as:
• V1 = IR1
• V2 = IR2

where I is the current through the circuit

Worked Example

The circuit is designed to light up a lamp when the input voltage exceed a preset value.
It does this by comparing Vout with a fixed reference voltage of 5.3 V.

Vout is equal to 5.3
Calculate the input voltage Vin.

Worked Example

A potential divider circuit consists of fixed resistors of resistance 5.0 Ω and 7.0 Ω connected in series with a 6.0 Ω resistor fitted with a sliding contact. These are connected across a battery of e.m.f 12 V and zero internal resistance, as shown.

What are the maximum and minimum output voltages of this potential divider circuit?

Exam Tip

Always make sure the correct resistance is in the numerator of the potential divider equation. This will be the resistance of the component you want to find the output voltage of.

Although both of the potential divider equations are given on the data sheet, make sure you’re comfortable with how to use them. Understanding each step in the worked examples will help with this.

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