2.44 Potential Dividers

• The electrical voltages rule is defined as:

The sum of the e.m.f.s in a closed circuit loop is equal to the sum of the potential differences around that loop

• Therefore, when two resistors are connected in series,  the potential difference across the power source will be divided across the two resistors

• Potential dividers are circuits that produce an output voltage as a fraction of the 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 three 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 link between the input voltage and the output voltage across each resistor is linked in an equation

Potential divider diagram and equation

• The input voltage V_in is applied across both resistors, which are in series
• The output voltage V_out is measured across one of the resistors, in this case resistor R₂
• The potential difference V across each resistor depends upon its resistance R:
  • The resistor with the largest resistance will have the greater potential difference across it
  • This is shown as a greater V_out
  • This is 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

• Since potential divider circuits are based on the ratio of voltage between components, and since V=IR, this is equal to the ratio of the resistances of the resistors
• Therefore, the ratios of the potential differences and resistances across each resistor can be linked

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