GCSE Physics Tutorial: Solving Problems for Circuits with Resistors in Series using Equivalent Resistance

11 Aug

Written By Seb Cox

In circuits with resistors connected in series, calculating the total resistance can become tedious when dealing with multiple resistors. However, the concept of equivalent resistance simplifies these calculations by combining the individual resistors into a single equivalent resistor. This tutorial will guide you through solving problems for circuits with resistors in series using the concept of equivalent resistance.

1. Understanding Series Circuits: In a series circuit, resistors are connected one after the other, forming a single path for current flow. The key property of series circuits is that the current remains constant throughout the circuit since it experiences the same resistance in each resistor.

2. Equivalent Resistance (R_eq): Equivalent resistance is a single resistance that represents the total opposition to current flow in a series circuit. When resistors are connected in series, the equivalent resistance (R_eq) is the sum of all individual resistances.

For two resistors (R₁ and R₂) in series:

R_eq = R₁ + R₂

For three resistors (R₁, R₂, and R₃) in series:

R_eq = R₁ + R₂ + R₃

And so on for any number of resistors in series.

3. Steps to Solve Problems: Follow these steps to solve problems for circuits with resistors in series using the concept of equivalent resistance:

Step 1: Identify the Resistors in Series:

Examine the circuit diagram and identify the resistors connected in series. Resistors in series have their terminal ends connected to each other.

Step 2: Calculate the Equivalent Resistance (R_eq):

Add up the resistances of all the resistors in series to find the equivalent resistance:
```
R_eq = R₁ + R₂ + R₃ + ...
```

Step 3: Apply Ohm's Law:

If the circuit has a power supply (battery or voltage source) and you are given the potential difference (voltage) across the circuit, use Ohm's law to calculate the current (I):
```
I = V / R_eq
```

Step 4: Analyse the Circuit:

Use the calculated equivalent resistance and current to analyse the circuit further. For example, you can determine voltage drops across individual resistors, power dissipation, or total circuit current.

4. Example Problem: Consider the following series circuit with three resistors:

[Power Supply] --- [R₁] --- [R₂] --- [R₃] --- [Negative Terminal]

Given: R₁ = 5 Ω, R₂ = 10 Ω, R₃ = 8 Ω, V (potential difference) = 12 V

Solution:

Calculate the equivalent resistance (R_eq):

R_eq = R₁ + R₂ + R₃
R_eq = 5 Ω + 10 Ω + 8 Ω
R_eq = 23 Ω

Calculate the current (I) using Ohm's law:

I = V / R_eq
I = 12 V / 23 Ω
I ≈ 0.52 A (Amperes)

5. Practical Applications:

The concept of equivalent resistance is invaluable in simplifying circuit calculations and analysing the behaviour of circuits with multiple resistors in series.
It is commonly used in electronics, household electrical circuits, and electrical engineering applications.

6. Summary: Solving problems for circuits with resistors in series becomes more manageable using the concept of equivalent resistance. By combining individual resistors into a single equivalent resistor, you can streamline calculations and understand the behaviour of series circuits more effectively. This concept is a fundamental tool in circuit analysis and design, providing a deeper understanding of electrical circuits.

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