Calculating Current in a Circuit with Series and Parallel Resistors

When working with electrical circuits, it is essential to understand how to calculate the current I flowing through resistors connected either in series or in parallel. This article will explore the formulas and process for calculating current in these configurations, specifically when resistors of 4 ohms and 6 ohms are driven by a 12V battery.

Understanding Series and Parallel Configurations

In a series configuration, resistors are connected end-to-end in a single path, causing the same current to flow through each resistor. In a parallel configuration, resistors are connected across the same two points, allowing the current to split and flow through multiple paths.

Series Configuration

In a series configuration, the total resistance Rtotal is the sum of the individual resistances:

Rtotal R1 R2

Using the given resistances of 4 ohms and 6 ohms:

Rtotal 4 Ω 6 Ω 10 Ω

Applying Ohm's Law, ( V I cdot R ), to find the current:

I

12 V

10 Ω

≈ 1.2 A

Parallel Configuration

In a parallel configuration, the total resistance Rtotal is calculated using the formula:

1/Rtotal 1/R1 1/R2

Substituting the values for the resistors:

1/Rtotal 1/4 Ω 1/6 Ω

Finding a common denominator (24) to add the fractions:

1/Rtotal (6 4)/24 10/24

Rtotal 24/10 2.4 Ω

Now, applying Ohm's Law to find the total current:

I

12 V

2.4 Ω

5 A

Summary

When the resistors are in series, the current is 1.2 A, and when they are in parallel, the current is 5 A.

Note that the configuration (series or parallel) must be specified to accurately determine the current.

Additional Considerations

Understanding the behavior of resistors in series and parallel configurations is crucial for anyone involved in electronics and electrical circuits. The correct application of these principles ensures the safe and efficient operation of systems. Remember that the laws of physics, particularly Ohm's Law, are key to deriving the current in any electrical setup.

Do you have any further questions or need assistance with calculating current in other circuit configurations?

Keywords: resistors in series, resistors in parallel, Ohm's Law