⇒ Potential dividers are simple, three-component circuits designed to control the potential difference in a circuit

⇒ They consist of a power supply (such as a cell); a fixed resistor; and a third resistive component, whose resistance can be fixed (fixed resistor) or variable (variable resistors, thermistors, light-dependent resistors, etc.)

⇒ All of these components are connected in series nd the emf of the power supply is shared across the two resistive components

⇒ The clue to how potential dividers work is in their name, potential dividers i.e. something that splits up potential difference - see the following example:

⇒ Generally we are trying to vary the potential difference V₁ (across R₁) by varying R₂

⇒ Assuming that the cell has negligible internal resistance, then the total resistance of the circuit R_T is given by: R_T = R₁ + R₂

⇒ From this equation it can be seen that if ε and R₁ are fixed, then V₁ only depends on R₂. In fact, as R₂ increaes, V₁ decreases, and vice versa

⇒ Another use of the potential divider is in sensor circuits

• If the variable resistor, R₂, in the potential divider circuit below is replaced with a component whose resistance varies with an external physical variable such as temperature or light intensity, then the potential difference across the fixed resistor, R₁, will also vary with the external physical variable

⇒ The voltemeter connected across R₁ can then be calibrated in terms of the value of the external physical variable

• The circuit can then be made to act as an electronic thermometer or an electronic light sensor

⇒ With an electronic thermometer, a thermistor is connected in place of R₂

• Most thermistors are ntc (negative temperature coefficient) thermistors
• This means that as the temperature increases, their resisstance decreases, as shown below:

⇒ The effect on the potential difference across the fixed resistor R₁ is that as the temperature increases, so the resistance of the thermistor, R₂, drops and V₁ rises

• Thus increasing temperature produces increasing potential difference
• If the voltmeter is connected acrosss the thermistor, the opposite will happen: increasing the temperature will produce a decrease in potential difference

⇒ A similar effect involves the use of a light-dependent resistor (LDR)

• These are components that change their resistance with light intensity, which makes them incredibly useful as light sensors
• LDRs are made of semi-conducting materials; as the light shines on the material electrons are freed from the structure and can flow through it, reducing the resistance of the LDR

⇒ In the dark, LDRs can have a very high resistance, of the order of megaohms, and yet in the light their resistance can drop as low as a few hundred ohms

⇒ If an LDR is connected into a potential divider in place of R₂ in the potential divider circuit then, as the light intensity increases, then so will the outpute potential difference V₁ across the fixed resistor

⇒ Also see our notes on:

• Electrical Power in Circuits
• Circuit Calculations
• Internal Resistance and Electromotive Force
• Potential Dividers