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:
  • I₁ = V₁/R₁

• Current through cell:
  • I_in = V_in/R_total = V_in/(R₁ + R₂)

• Since I₁ = I_in then:
  • V₁/R₁ = V_in/(R₁ + R₂)
• If we rearrange this, we have:
  • V₁ = V_in x (R₁/(R₁ + R₂))

• Since V_out = V_1, we have:
  • V_out = V_in x (R₁/(R₁ + R₂))
  • This is the potential divider equation.
  • 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

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:
  • https://www.saburchill.com/physics/images_practicals/resistors_01.jpg
  • or will use sensor resistors such as thermistors or LDRs like this: http://iamtechnical.com/sites/default/files/voltage-divider-cold-sensor.jpg
  • 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 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).