Resistors in Parallel (Cambridge (CIE) AS Physics)

Deriving the equation for 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 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:

Resistors in parallel

• When two or components are connected in parallel:

  The reciprocal of the combined resistance is the sum of the reciprocals of the individual resistances

Resistors in parallel

Resistors connected in parallel have the same voltage

• The equation for the combined resistance, R  of resistors in parallel is:

• 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 

• For example, the reciprocal of a whole number such as 2 equals 

  • The reciprocal of  is 2

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

Reciprocals

The reciprocal of a number is 1 ÷ number

• In the case for the resistance R, this becomes . To get the value of R from , you must calculate

• You can also use the reciprocal button on your calculator (labelled either x^-1 or , depending on your calculator