How To calculate Resistors Connected In Series And Parallel

How To calculate Resistors Connected In Series And Parallel

Resistors can be connected in series or in parallel. Each type of connection has different way of calculating its total equivalent resistance.

In this article you will learn:

  • How to calculate the total equivalent resistance of resistors connected in series.
  • The effect of resistors  in series.
  • How to calculate the total equivalent resistance of resistors connected in parallel.
  • The effect of resistors in parallel.

 

Resistors In Series

Resistors are said to be connected in “ Series “, if it is connected end-to-end within a circuit or together in a single line. Resistors in series have the same amount of current passing through them but have different voltage in them. We can calculate the voltage in each resistor by using voltage divider theorem. The amount of current is the same for a set of resistors connected in series.

For resistors connected together in series, the total resistance or the total equivalent resistance of the circuit must be equal to the sum of all the individual resistors added together i.e by taking the individual resistive values. The equivalent resistance of a circuit is the single value of resistance that can replace any number of resistors in series without changing the values of the voltage or the current in the circuit.

Note: The equivalent or total resistance has the same effect on the circuit as the original combination of resistors.

Resistors In Series

Series Resistor Equation

If two resistors in series have the same resistive value,let say 1KΩ (1000 ohms) , then the equivalent resistance will be 1KΩ + 1KΩ = 2KΩ. If three resistors in series are unequal and of different values, then the total or equivalent resistance, R is equal to the mathematical sum of the three resistances. That is equal to R + R + R. If four or more unequal (or equal) resistors are connected in series then the equivalent resistance is: R + R + R + R +….. etc. One essential point to note about resistors in series is that the total equivalent resistance of two or more will always be greater than the value of the largest resistor in the network.

Example

Resistors In Series

The equivalent resistance of the resistors in the diagram will be 500 + 900 + 600 = 2000 (2KΩ)

 

Resistors In Parallel

Resistors are said to be connected in parallel if there are multiple paths for the flow of current in the parallel network. Resistors connected in parallel have the same voltage across them but have different amount of current flowing through them. Resistors in parallel are connected to the same two points (nodes) to a common voltage source. In order to calculate the current flowing in each resistor connected in parallel, current divider theorem is used.

Resistors in parallel

 

Parallel Resistor Equation

For resistors in parallel the equivalent resistance R is calculated differently unlike the ones connected in series. Here, the reciprocal ( 1/R ) value of the individual resistances value are all added together. The inverse of the equivalent resistance of two or more resistors connected in parallel is the algebraic sum of the inverses of the individual resistances. If the two resistances in parallel are equal (the same value, let say 1KΩ and 1KΩ) Then the equivalent resistance, R is equal to half (500Ω) the value of one of the resistors. That is 1/R =1/1000 + 1/1000 = 500

For three equal resistors in parallel, it is one-third (R/3) the value of one of the resistors,etc. It is important to note that the equivalent resistance is always less than the smallest resistor in the parallel network of resistors. Therefore, the total resistance, R will always decrease as more parallel resistors are added.

 

Example

resistors in parallel

The equivalent resistance of the resistors above will be 1/R = 1/3 + 1/2 + 1/5 = 0.968 (968mΩ), mΩ means milliohms.

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