how to find equivalent resistance between points a and b

"Equivalent Resistance: A to B Calculation Guide"

By David BrownDecember 1, 2025

In the realm of electronics, understanding how to find equivalent resistance between two points, say A and B, is a fundamental skill. This process, known as finding the equivalent resistance or total resistance, helps us analyze complex circuits by simplifying them into a single resistor. Let's dive into the methods to achieve this, ensuring your circuits are always well-understood and optimized.

Understanding Series and Parallel Resistances

Before we delve into finding equivalent resistance, it's crucial to grasp the basics of series and parallel resistances. These are the two primary ways resistors can be connected in a circuit.

Series Connection: Resistors are connected end-to-end. The current flowing through each resistor is the same, but the voltage drops across them add up.
Parallel Connection: Resistors are connected side-by-side. The voltage across each resistor is the same, but the currents divide among them.

Finding Equivalent Resistance in Series

In a series circuit, the total resistance (R_total) can be found by simply adding up the individual resistances (R₁, R₂, ..., R_n). The formula is:

the equivalient resistance between points a and b in the circuit shown is

R_total = R₁ + R₂ + ... + R_n

Example:

Consider a series circuit with three resistors: R₁ = 10Ω, R₂ = 20Ω, and R₃ = 30Ω. The total resistance would be:

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R_total = 10Ω + 20Ω + 30Ω = 60Ω

Finding Equivalent Resistance in Parallel

Finding the equivalent resistance in a parallel circuit is a bit more complex. The formula is:

1/R_total = 1/R₁ + 1/R₂ + ... + 1/R_n

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Or, equivalently:

R_total = 1 / (1/R₁ + 1/R₂ + ... + 1/R_n)

Example:

Let's consider a parallel circuit with the same three resistors: R₁ = 10Ω, R₂ = 20Ω, and R₃ = 30Ω. The total resistance would be:

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1/R_total	=	1/10Ω + 1/20Ω + 1/30Ω
R_total	=	1 / (1/10Ω + 1/20Ω + 1/30Ω)
	=	1 / (0.1 + 0.05 + 0.0333)
	=	1 / 0.1833 ≈ 5.45Ω

So, the total resistance in this parallel circuit is approximately 5.45Ω.

Finding Equivalent Resistance in Complex Circuits

In more complex circuits, you might need to simplify the circuit by finding the equivalent resistance of a group of resistors and then continuing the process with the simplified circuit. This is where understanding series and parallel resistances becomes crucial.

Remember, the key to finding equivalent resistance lies in identifying the type of connection (series or parallel) and applying the appropriate formula. With practice, this process will become second nature, enabling you to analyze and optimize circuits with ease.