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, R₁ and R₂2, are in series, the total resistance, R_t, is given by the following formula.

R_t = R₁ + R₂

If the same resistors are in parallel, the total resistance is as follows:

R_t = 1/R₁ + 1/R₂

E.g. 1

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

R_t = R₁ + R₂

R_t = 6 + 3

R_t = 9

E.g.2

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

1/R_t = 1/10 + 1/15

1/R_t = 5/30

R_t = 6

If 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