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 equation for combined resistors in parallel 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