Substitution Theorem & Examples

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Substitution Theorem defenition circuit theorem

Substitution Theorem: The Substitution Theorem is used in circuit analysis to simplify complex networks by replacing a branch (like a resistor) with an equivalent voltage or current source, provided the voltage across or current through that branch remains identical, thus keeping the rest of the circuit’s behavior (voltages/currents) unchanged.

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Substitution Theorem

Read Also: Reciprocity Theorem

Defenition


In a linear network, any passive element can be replaced by a voltage source whose magnitude is the drop across that element, and the polarity of the source is the drop polarity across that element, provided the other branch currents and voltages are constant.

Substitution Theorem defenition circuit theorem
Substitution Theorem definition circuit theorem

Problem 1

For the circuit shown in the following figure, the 1 Ω resistor can be replaced by

Substitution Theorem problem circuit theorem
Substitution Theorem problem circuit theorem

Solution: Using the substitution theorem, the equivalent circuit can be represented as follows.

Substitution Theorem problem solution circuit diagram
Substitution Theorem problem solution circuit diagram

So 1 Ω resistor can be replaced with voltage source of 1 V with the positive terminal upwards.

Read: Reciprocity Theorem

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Books for All Competitive Exams

Electrical Circuit Theorems

  1. Substitution Theorem & Examples
  2. Reciprocity Theorem with Examples
  3. Duality Theorem in Electrical circuits

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