4.06 Resistors in series.

Introduction.
Ohm's law can be used to calculate the amount of current that will flow from a power supply, when it is connected to a single resistor, I = V/R.
However, in most circuits there will be more than one resistor and these resistors may be connected in different ways. In these circuits, before we can calculate the current that will flow from the power supply, we first need to calculate the combined resistance of the individual resistors in the circuit. In this section we will look at the two possible ways of connecting resistors together and how to calculate the total resistance in each case.

Series and parallel circuits.

Series circuits.

In a series circuit (which is a single loop), the current only has one path to flow through and the current will be the same at all points along this path.
As we have already seen from Kirchoff's voltage law, the sum of the voltage drops around the loop is equal to the voltage of the applied e.m.f.

Resistors in series.

The diagram below shows three resistors connected in series. To show how to calculate the total resistance, we will use Kirchoff's voltage law and ohms law.

resistors in series

According to Kirchoff's voltage law, the voltage of the e.m.f. is equal to the sum of the voltage drops across each resistor.

V_T = V₁ + V₂ + V₃ .

According to Ohm's law, V = IR. Therefore substituting for V gives;

IR_T = IR₁ + IR₂ + IR₃.
(R_T is the total resistance. I is the series current flowing through each resistor).

dividing both sides of the equation by I, gives;

R_T = R₁ + R₂ + R₃.

Therefore to find the total resistance of series resistors, we simply add the individual resistor values together.

R_T = R₁ + R₂ + R₃.