Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Resistance

## You may also like

### Hold Still Please

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Age 16 to 18

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

When resistances are connected in a line so that the current in the circuit has only one route to take the total resistance is the sum of the separate resistances. The resistances are said to be connected in series . In this diagram the total resistance $R$ is given by $R = R_1 + R_2 + R_3$. |

When resistances are connected in parallel so that, at a junction, the current flows along more than one route, the reciprocal of the total resistance is the sum of the reciprocals of the separate resistances. In this diagram the total resistance $R$ is given by $${1 \over R} = {1 \over R_1} + {1 \over R_2} + {1 \over R_3}.$$ |

Can you arrange a set of charged particles so that none of them start to move when released from rest?