⇒ When components are connected together to make useful circuits, each component adds a certain resistance to the circuit

⇒ The effect of the added resistance depends on how the component is connected into the circuit - in series with other components or in parallel (or both in the case of circuits containing many hundreds of components)

⇒ There are some simple rules for calculating the overall resistance of components connected in series or in parallel

⇒ Consider the resistor network shown below:

⇒ And the following represents the single resistor that could replace the three resistors in series in the circuit above:

⇒ Consider the following circuit:

⇒ In the right-hand circuit one resistor, R_T, has been used to replace all three resistors arranged in parallel in the left-hand circuit

⇒ Again, using Kirchoff's Circuit laws and the definition of resistance, V = IR:

⇒ In summary, for resistors connect in series the overall reistance is the sum of the individual resistors

⇒ For resistors in parallel the reciprocal of the overall resistance is the sum of all the reciprocal of the individual resistances

• Resistors connectedin parallel always have a resistance less than any of the individual resistors - this is a useful check when you have done a calculation

Three resistorrs are connected in parallel to a power supply as seen below. Calculate the value of the one resistor that could replace all three resistors

⇒ When calculating the overall resistance of a circuit containing a mixture of resistors in series and in parallel, it is best to calculate the overall resistance of each of the sections arranged in parallel first, and then calculate the overall resistance by summing all the effective resistances in series

Look at the combination circuit below, containing resistors connected in series and in parallel. What is the overall resistance of this circuit?

⇒ Also see our notes on:

• Electrical Power in Circuits
• Circuit Calculations
• Internal Resistance and Electromotive Force
• Potential Dividers