Series and parallel circuits

Resistor in series

When resistors are connected in series, the current through each resistor is the same. In other words, the current is the same at all points in a series circuit.

When resistors are connected in series, the total potential difference across all the resistors is equal to the sum of the potential differences across each resistor.

In other words, the potential differences around the circuit add up to the potential difference of the supply.

The total resistance of a number of resistors in series is equal to the sum of all the individual resistances.

In the circuit above, the following applies

• I₁ = I₂ = I₃
• V_T = V₁ + V₂ + V₃

And so, therefore, R_T = R₁ + R₂ + R₃

Resistors in parallel

When resistors are connected in parallel, the supply current is equal to the sum of the currents through each resistor. In other words the currents in the branches of a parallel circuit add up to the supply current.

When resistors are connected in parallel, they have the same potential difference across them. In other words, any components in parallel have the same potential difference across them.

For the circuit above, the formula for finding the total resistance of resistors in parallel is 1/R_T = 1/R₁ + 1/R₂ + 1/R₃

• I_T = I₁ + I₂ + I₃
• V₁ = V₂ = V₃

And so 1/R_T = 1/R₁ + 1/R₂ + 1/R₃