Equivalent Resistance Formula: Series And Parallel Circuit Example

Equivalent Resistance formula of an object is the measure of how much it opposes the flow of current. It is calculated in ohms. The amount of opposition to the flow of current can be increased by combining two or more resistances in a series or parallel arrangement. 

Key Terms: Equivalent Resistance, Equivalent Resistance Calculator, Formula of Equivalent Resistance, Equivalent Resistance Formula in Parallel, Equivalent Resistance in Series

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What is Equivalent Resistance? 

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Equivalent Resistance refers to the point where the total resistance of a series or parallel arrangement is calculated. There are separate formulae to calculate equivalent resistance for series and parallel arrangements respectively. 

• Either the whole circuit or in a part of the circuit.
• Equivalent resistance is defined between nodes or two terminals of the network.
• Single resistor can substitute the complete network for a specified voltage and the current can be obtained when used as a network.
• If a lot of energy is required then the resistance necessary will also be high. The equivalent resistance of a network is a single resistor which can replace the entire network.
• The applied voltage (V) will be the same as current (I).

Equivalent Resistance

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Series Arrangement of Resistance

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Series Arrangement refers to the arrangement of resistors in which all the resistors are connected in one line. The total resistance of such an arrangement is the sum of each resistance. 

R_S = R₁ + R₂ + R₃ + ……. 

The series arrangement of resistors is implied to improve/increase the total resistance. 

Resistance formula for series arrangement

Example: Two 6-Ω resistors are connected in series, they are equivalent to having one 12-Ω resistor in the circuit. This is the concept of equivalent resistance in a series circuit.

Example of Series Arrangement of Resistance

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Parallel Arrangement of Resistance 

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Parallel Arrangement refers to the arrangement of resistors in which all the resistors are connected parallel to each other. The reciprocal of the total resistance of such an arrangement is the sum of the reciprocal of each resistance. 

1 / R_P = 1 / R₁ + 1 / R₂ + 1 / R₃ + ……. 

The parallel arrangement of resistors is implied to decrease the total resistance.

Resistance formula for Parallel Resistance

Example: Two resistors positioned in parallel branches, both of them have the same resistance value of 4. The circuit has two equivalent paths for the charge transport but, just one-half of the charge can choose to travel through the branch.

Parallel Arrangement of Resistance

The branch gives 4Ω of resistance to any charge flowing through it and only ½ of all the charge flowing through the circuit may meet 4Ω of resistance of that branch. Hence, the presence of two 4Ω resistors in parallel will be equal to one 2Ω resistor in the circuit.This is the concept of equivalent resistance in a parallel circuit.

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Things to Remember

• The resistance of an object is the measure of how much it opposes the flow of current. It is calculated in ohms.
• Equivalent Resistance refers to the point where the total resistance of a series or parallel arrangement is calculated.
• Series Arrangement refers to the arrangement of resistors in which all the resistors are connected in one line. 
• The total resistance of the series arrangement is the sum of each resistance.
• Parallel Arrangement refers to the arrangement of resistors in which all the resistors are connected parallel to each other. 
• The series arrangement of resistors is implied to improve/increase the total resistance.
• The parallel arrangement of resistors is implied to decrease the total resistance.

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Previous Year Questions

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