Parallel Circuits: Dividing Current

In a parallel circuit, components are connected in separate branches, providing multiple paths for the current to flow. This means that the current divides among the different branches based on their respective resistances.

Key Concepts

• In a parallel circuit, the total resistance is calculated differently than in a series circuit.
• The voltage across each branch in a parallel circuit is the same.
• The total current in a parallel circuit is the sum of the currents flowing through each branch.

Formula

The total resistance (R_total) of a parallel circuit can be calculated using the following formula:

where $R_1, R_2, R_3, ..., R_n$ are the individual resistances of the branches.

Example

Let's consider a parallel circuit with three branches: R1 = 10 ohms, R2 = 20 ohms, and R3 = 30 ohms. The total resistance can be calculated as follows:

To find $R_\text{total}$, we can take the reciprocal of the sum of the reciprocals:

Therefore, the total resistance of the circuit is 10 ohms.

Illustration (TODO)

Here is an illustration of a parallel circuit:

In the illustration, you can see that the components (represented by resistors) are connected in separate branches, providing multiple paths for the current to flow. The voltage (represented by + and - symbols) across each branch is the same, and the current divides among the different branches.

Summary

In a parallel circuit, components are connected in separate branches, allowing the current to divide among them. The total resistance of a parallel circuit is calculated differently than in a series circuit. Understanding parallel circuits is important for analyzing and designing electrical circuits.

Next, let's explore circuit analysis techniques that help in solving more complex circuits.