Electricity and Magnetism: Resistors in Series and in Parallel


Resistors that also symbolize electrical devices such as lamps and hair dryers can be connected to a potential difference (electric outlet or battery) by two main types of circuits:

  • Series
  • Parallel

The type of connection used in designing an electric circuit depends on the purpose and properties of the devices to be connected. Reviewing these properties is the main purpose of this lesson.


Resistors in a Series Circuit

Below is a schematic diagram of resistors connected in a series circuit. Notice that the resistors connect end to end along a single path (loop).

In a series circuit, , that is the total (equivalent) resistance is the algebraic sum of all resistances.

Electric current through each resistor has the same magnitude . We can reach this conclusion by noticing that there is only one path that the electrons can flow through. In order to calculate the current (which can also be thought of as the number of electrons) the equivalent resistance of the entire circuit must be calculated first. If the potential difference on the battery is ΔVBattery then by Ohm’s law, we have:

Notice that if more resistors are being connected in series, the current respectively decreases in the entire circuit.


Calculating Potential Drop (Difference) on Each Resistor

Each resistor must receive a certain amount of electric energy to function properly. The energy can be seen as the voltage coming from the battery. The voltage must be then distributed among all resistors. How much potential is used by each resistor depends on each resistor’s individual resistance. The higher the resistance (in ohms, Ω), the higher the potential drop, thus the higher usage of energy. The energy is due to the voltage and current flowing, so applying Ohm’s law, we have respectively

Notice that

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