Resistors in Parallel (Cambridge (CIE) AS Physics): Revision Note

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:

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}...$

• 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 $\frac{1}{value}$

• For example, the reciprocal of a whole number such as 2 equals $\frac{1}{2}$

  • The reciprocal of $\frac{1}{2}$ 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 $\frac{1}{R}$. To get the value of R from $\frac{1}{R}$, you must calculate $\frac{1}{youranswer}$

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