Potential Dividers

Potential Dividers

Many students are confused by Potential Dividers but this need not be the case.

A potential divider is a circuit which uses two resistors or a rheostat (variable resister) with a moveable contact. A potential divider does literally what it says: divides potential or splits voltage in colloquial terms in order to power a device at a lower voltage than the supply.

If you struggle with potential divider questions, remember: circuit rules (based on Kirchoff s Laws) ALWAYS apply:

Components connected in series will always have the same current.

Components connected in parallel will always have the same potential difference (voltage)

In a simple series circuit, the EMF (supply voltage) is shared between the components.

Here is a simple potential divider circuit:

http://physicsnet.co.uk/wp-content/uploads/2010/08/potential-divider.jpg

The two resistors are connected in series with the cell. Resistor R₁ has a voltmeter connected across it. What does this tell us?

The current through the cell and each of the two resistors is the same since they are connected in series.

The sum of the potential difference (voltage) across each resistor must equal the cell terminal p.d. (supply voltage) V_in since the cell and resistors form a simple series circuit.

The voltmeter reading (V_out) will show the p.d. across resistor R₁ (V₁) since it is connected in parallel with R₁.

Let s look at this first point:

Current through resistor R₁:

o I₁ = V₁/R₁

Current through cell:

o I_in = V_in/R_total = V_in/(R₁ + R₂)

Since I₁ = I_in then: o V₁/R₁ = V_in/(R₁ + R₂)

o If we rearrange this, we have:

o V₁ = V_in x (R₁/(R₁ + R₂))

Since Vout lt;/sub>= V_1, we have:

o V_out = V_in x (R₁/(R₁ + R₂))

o This is the potential divider equation.

o Sometimes you will see R₁ R₂ swapped but this does not affect the underlying physics.

If the voltmeter is replaced with a component such as a bulb or motor (sometimes called the load), it will be powered at the same p.d. V_out.

Some important points to remember:

Outside the laboratory a potential divider won t use two fixed resistors. It will have a rheostat with a floating connection like this:

o https://www.saburchill.com/physics/images_practicals/resistors_01.jpg

o or will use sensor resistors such as thermistors or LDRs like this: http://iamtechnical.com/sites/default/files/voltage-divider-cold-sensor.jpg

o or this: https://www.yenka.com/activities/Potential_Dividers_and_Sensors/attachments/Potential%20Dividers%20and%20Sensors%20-%20Model1.gif

When correctly used, the load (component connected across R₁) should have a much higher resistance than R_1. This is so that the load draws negligible current from the circuit.

If the load resistance is not sufficiently high then it will create a parallel resistor combination with a total resistance lower than R₁ which must be calculated using the parallel resistor equation: (1/R_total) = (1/R₁) + (1/R₂).