Formulae

Ohm’s law is one of the most important laws of electrical circuits. It states that the current passing through a conductive material, eg a resistor, is equal to voltage divided by resistance. Ohm’s triangle can be used to remember three important equations:

Three triangles to represent how Ohm's law can be used to calculate current (voltage over resistance), resistance (voltage over current) and voltage (current times resistance).
  • voltage (V) - the potential difference between two points, measured in volts (V)
  • current (I) - the flow of electricity around a circuit, measured in amps (A)
  • resistance (R) - how easily electricity flows through a wire, measured in ohms (Ω)

Resistors in series

Sometimes more than one resistor is used in a circuit. To calculate the combined resistance, each resistor’s value should be added together:

Three resistors in series (one after the other in a line) labelled from left to right R1, R2 and R3.

Resistance or Rtotal = R1 + R2 + R3

Example

What is the total value of resistors below?

Three resistors in series (one after the other in a line) labelled from left to right 10 Ohms (Ω), 22 Ohms (Ω) and 2,200 Ohms (Ω) for calculating resistance.

Rtotal = R1 + R2 + R3

= 10 + 22 + 2,200

= 2,232 Ω

Question

What is the total value of resistors below?

Three resistors in series (one after the other in a line) labelled from left to right 24 Ohms (Ω), 31 Ohms (Ω) and 1,500 Ohms (Ω) for calculating resistance.

Rtotal = R1 + R2 + R3

= 24 + 31 + 1500

= 1,555 Ω

Resistors in parallel

When resistors are placed in a parallel arrangement, the resistors are in parallel - the current is shared between each junction.

Resistance or 1/Rtotal = 1/R1 + 1/R2 + 1/R3

Three resistors in parallel (one beneath the other joined in a circuit) labelled from top to bottom R1, R2 and R3.

Example

What is the total resistance for the circuit below?

Three resistors in parallel (one beneath the other joined in a circuit) labelled from top to bottom 6 Ohms (Ω), 3 Ohms (Ω) and 9 Ohms (Ω) for calculating resistance.

1/Rtotal = 1/R1 + 1/R2 + 1/R3

= 1/6 + 1/3 + 1/9

Give them a common denominator:

= 3/18 + 6/18 + 2/18

1/Rtotal = 11/18

Therefore, 11Rtotal = 18

Rtotal = 18/11

= 1.64 Ω

Question

What is the total resistance for the circuit below?

Three resistors in parallel (one beneath the other joined in a circuit) labelled from top to bottom 8 Ohms (Ω), 24 Ohms (Ω) and 4 Ohms (Ω) for calculating resistance.

1/Rtotal = 1/R1 + 1/R2 + 1/R3

= 1/8 + 1/24 + 1/4

Common denominator:

= 3/24 + 1/24 + 6/24

1/Rtotal = 10/24

Therefore, 24Rtotal = 10

Rtotal = 10/24

= 0.42 Ω