Deriving Equations for Resistance in Series & Parallel
Resistors In Series
- When two or more components are connected in series:
- The combined resistance of the components is equal to the sum of individual resistances
Resistors connected in series
- The equation for combined resistors in series is derived using the electric current rule and the electrical voltages rule
- These rules describe that for a series circuit:
- The current is the same through all resistors
- The potential difference is split between all the resistors
- The equation for the combined resistance of resistors in series is therefore:
Resistors In Parallel
- In a parallel circuit, the combined resistance of the components requires the use of reciprocals
- the reciprocal of the combined resistance of two or more resistors is the sum of the reciprocals of the individual resistances
Resistors connected in parallel
- the reciprocal of the combined resistance of two or more resistors is the sum of the reciprocals of the individual resistances
- The equation for combined resistors in series is derived using the electric current rule and the electrical voltages rule
- These rules describe that for a parallel circuit:
- The current is the split at the junction (and therefore between resistors)
- The potential difference is the same across all resistors
- The equation for the combined resistance of resistors in parallel is therefore:
- This means the combined resistance decreases
- The combined resistance 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
Using Equations for Resistance in Series & Parallel
Series Circuits
Worked Example
The combined resistance R in the following series circuit is 60 Ω.
Wich of the following is the value of R2?
A. 100 Ω B. 30 Ω C. 20 Ω D. 40 Ω
Parallel Circuits
Worked Example
Exam Tip
The most common mistake is to forget to find the correct value for RT in parallel. Remember to do 
to get the correct value.
Reciprocals can be considered in the following way:
- The reciprocal of a value is
- For example, the reciprocal of a whole number such as 2 equals
- The reciprocal of is 2
- For example, the reciprocal of a whole number such as 2 equals
- 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 of the resistance R, this becomes
- To get the value of R from , you must do
- To get the value of R from
- You can also use the reciprocal button on your calculator (labelled either x-1 or
, depending on your calculator)
