
Table of Contents
 Find the Equivalent Resistance Between A and B
 Understanding Resistance
 Series and Parallel Resistors
 Series Resistors
 Parallel Resistors
 Combining Series and Parallel Resistors
 Step 1: Simplify Series and Parallel Sections
 Q&A
 Q1: Can the equivalent resistance ever be lower than the smallest resistor in a circuit?
 Q2: What happens if all resistors in a parallel configuration have the same resistance?
When it comes to analyzing electrical circuits, one common task is to determine the equivalent resistance between two points. This is particularly useful in situations where multiple resistors are connected in various configurations, such as series or parallel. By finding the equivalent resistance, we can simplify the circuit and make further calculations or analysis easier. In this article, we will explore different methods and techniques to find the equivalent resistance between points A and B, providing valuable insights and examples along the way.
Understanding Resistance
Before diving into finding the equivalent resistance, let’s first understand what resistance is. Resistance is a fundamental property of any material that opposes the flow of electric current. It is measured in ohms (Ω) and denoted by the symbol R. The higher the resistance, the more difficult it is for current to flow through a material.
Resistance can be influenced by various factors, including the length and crosssectional area of a conductor, as well as the material’s resistivity. Different materials have different resistivities, which determine their inherent resistance. For example, copper has a lower resistivity compared to steel, making it a better conductor of electricity.
Series and Parallel Resistors
When resistors are connected in a circuit, they can be arranged in two common configurations: series and parallel.
Series Resistors
In a series configuration, resistors are connected endtoend, forming a single path for current to flow through. The total resistance in a series circuit is the sum of the individual resistances. Mathematically, we can express this as:
R_{eq} = R_{1} + R_{2} + R_{3} + … + R_{n}
For example, let’s consider a series circuit with three resistors: R_{1} = 10Ω, R_{2} = 20Ω, and R_{3} = 30Ω. The equivalent resistance can be calculated as:
R_{eq} = 10Ω + 20Ω + 30Ω = 60Ω
Parallel Resistors
In a parallel configuration, resistors are connected side by side, providing multiple paths for current to flow through. The total resistance in a parallel circuit can be calculated using the following formula:
1/R_{eq} = 1/R_{1} + 1/R_{2} + 1/R_{3} + … + 1/R_{n}
Let’s consider a parallel circuit with three resistors: R_{1} = 10Ω, R_{2} = 20Ω, and R_{3} = 30Ω. The equivalent resistance can be calculated as:
1/R_{eq} = 1/10Ω + 1/20Ω + 1/30Ω
1/R_{eq} = 3/30Ω + 2/30Ω + 1/30Ω
1/R_{eq} = 6/30Ω
1/R_{eq} = 1/5Ω
R_{eq} = 5Ω
Combining Series and Parallel Resistors
In realworld circuits, it is common to have a combination of series and parallel resistors. To find the equivalent resistance in such cases, we need to apply a stepbystep approach.
Step 1: Simplify Series and Parallel Sections
The first step is to identify any series or parallel sections within the circuit and simplify them. By doing so, we can reduce the complexity of the circuit and make it easier to find the equivalent resistance.
Let’s consider a circuit with two resistors, R_{1} = 10Ω and R_{2} = 20Ω, connected in parallel. This parallel combination is then connected in series with another resistor, R_{3} = 30Ω. To find the equivalent resistance, we can simplify the parallel section first:
1/R_{eq1} = 1/R_{1} + 1/R_{2}
1/R_{eq1} = 1/10Ω + 1/20Ω
1/R_{eq1} = 3/30Ω + 2/30Ω
1/R_{eq1} = 5/30Ω
1/R_{eq1} = 1/6Ω
R_{eq1} = 6Ω
Now, we have simplified the parallel section and found the equivalent resistance as 6Ω. We can represent this simplified section as a single resistor with a resistance of 6Ω.
The circuit now becomes a series combination of R_{eq1} = 6Ω and R_{3} = 30Ω. To find the equivalent resistance of this series combination, we can simply add the resistances:
R_{eq} = R_{eq1} + R_{3}
R_{eq} = 6Ω + 30Ω
R_{eq} = 36Ω
Therefore, the equivalent resistance between points A and B in this circuit is 36Ω.
Q&A
Q1: Can the equivalent resistance ever be lower than the smallest resistor in a circuit?
A1: No, the equivalent resistance can never be lower than the smallest resistor in a circuit. The equivalent resistance is always greater than or equal to the smallest resistor. This is because resistors in parallel provide additional paths for current to flow, reducing the overall resistance. However, adding more paths will never decrease the resistance below the value of the smallest resistor.
Q2: What happens if all resistors in a parallel configuration have the same resistance?
A2: If all resistors