### Total resistance of combined resistors - series and parallel circuits

Resistors in series and parallel |

Resistors can be combined in two different methods; they are in series and in parallel.

If two resistors, R

_{1}and R_{2}2, are in series, the total resistance, R_{t}, is given by the following formula.R

_{t}= R_{1}+ R_{2}If the same resistors are in parallel, the total resistance is as follows:

R

_{t}= 1/R_{1}+ 1/R_{2}E.g. 1

Two resistors, 6 and 3 are connected in series. Find the total resistance.

R

_{t}= R_{1}+ R_{2}R

_{t}= 6 + 3R

_{t}= 9E.g.2

Two resistors, 10 and 15 are in parallel. Find the total resistance.

1/R

_{t}= 1/10 + 1/151/R

_{t}= 5/30R

_{t}= 6If resistors are in series

- The total resistance is bigger than the highest individual resistance of the circuit.
- The current through each resistor is the same.
- The total voltage splits up across each resistor.
- If one resistors is removed, the currents does not flow through the entire circuit

E.g. Christmas tree decorating lights

If resistors are in parallel

- The total resistance is smaller than the highest individual resistance of the circuit.

- The voltage across each resistor is the same.
- The total current splits up across each resistor
- The loss of a resistor does not affect the functioning of the circuit

E.g. The domestic electric circuits

You can practise the resistors in series and parallel with the following applet:

For a more comprehensive tutorial with lots of worked examples on electricity, please use the following link on the main site:

Electricity tutorial

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