10.1.8 Resistors in Parallel

• In a parallel circuit, the reciprocal of the combined resistance of two or more resistors is the sum of the reciprocal of the individual resistances
• In a parallel circuit:
  • The current is the split at the junction (and therefore between resistors)
  • The potential difference is the same through all resistors

• The equation for combined resistors in parallel is derived using Kirchhoff’s laws:

• When two or component are connected in parallel:
  • The reciprocal of the combined resistance is the sum of the reciprocals of the individual resistances

Resistors connected in parallel

Combined resistance of two or more resistors in parallel equation

• This means the combined resistance decreases and is less than the resistance of any of the individual components
• For example, If two resistors of equal resistance are connected in parallel, then the combined resistance will halve

Maths tip

• The reciprocal of a value is 1 / value
• For example, the reciprocal of a whole number such as 2 equals ½
  • The reciprocal of ½ is 2

• If the number is already a fraction, the numerator and denominator are ‘flipped’ round

The reciprocal of a number is 1 ÷ number

• In the case for the resistance R, this becomes 1/R. To get the value of R from 1/R, you must do 1 ÷ your answer
• You can also use the reciprocal button on your calculator (labelled either x^-1 or 1/x, depending on your calculator