Why Do Parallel Resistors Add Up in Voltage When They Should See the Same Voltage?

One of the common points of confusion in electrical circuits is the behavior of identical resistors connected in parallel. Contrary to the intuition that all parallel resistors should see the same voltage, one often wonders why the voltages of two or more identical resistors seem to be added together under certain circumstances. This article aims to clarify this point by examining the underlying principles of parallel circuits and voltage division.

Understanding Voltage in Parallel Circuits

In a parallel circuit, each resistor sees the same voltage as the source, regardless of the number of resistors in parallel. This is a fundamental principle in electrical engineering and can be easily demonstrated using Ohm's Law:

Voltage (V) Current (I) × Resistance (R)

When resistors are connected in parallel, the voltage across each resistor is the same as the total voltage supplied by the source. Therefore, the voltage across each resistor is independent of the resistance value, provided they are connected to the same voltage source.

Why Aren't Resistors in Parallel Voltage-Added?

The key to understanding this is recognizing that the voltage across resistors in parallel is not inherently added. However, the current through each resistor can add up depending on the circuit configuration. Here's a detailed explanation:

Configuration 1: All Resistors Connected to the Same Voltage Source

Consider a simple circuit with two identical resistors (R1 and R2) connected in parallel to a voltage source (V). According to Ohm's Law, the voltage across both R1 and R2 is V:

VR1 VR2 V

Even though the resistors are in parallel, each one sees exactly V, the same voltage as the source. There is no addition of voltages here; rather, the same voltage is distributed evenly across all parallel resistors.

Configuration 2: Series Addition of Voltages

When resistors are arranged in a series configuration, the total voltage is the sum of the individual voltages across each resistor. For example, consider two resistors R1 and R2 connected in series to the same source voltage V:

Total Voltage VR1 VR2

If R1 and R2 have the same resistance value, let's say R, then:

VR1 VR2 IR

Here, the total voltage V is the sum of the individual voltages:

V VR1 VR2 IR IR 2IR

This is because the current through both resistors is the same (Kirchhoff's Current Law), and the voltage drops add up along the series path.

Clarifying the Misconception

A common misconception arises when one thinks that parallel resistors somehow "add up" the voltage due to their parallel configuration. However, the voltage remains the same across all resistors in parallel. The confusion may arise when dealing with complex circuits or misunderstandings of circuit analysis principles.

Practical Applications and Analysis

Understanding the behavior of parallel resistors is crucial for designing and analyzing various electrical circuits. For example, consider a load-sharing circuit where multiple identical loads (resistors) are connected in parallel to a power supply:

Example: Load-Sharing Circuit

In a load-sharing circuit, such as a power supply connected to multiple identical devices (resistors in parallel), the voltage remains constant across each device:

Configuration: 5 Identical Resistors in Parallel

VR1 VR2 VR3 VR4 VR5 V

Each resistor sees the same voltage V, and the total current is the sum of the currents through each resistor:

Total Current IR1 IR2 IR3 IR4 IR5

Since each resistor has the same resistance (R), the current through each resistor is:

IR1 IR2 IR3 IR4 IR5 V/R

The total current is therefore 5 times the current through one resistor:

Total Current 5(V/R) 5I

This is an example of how series addition of currents in parallel circuits can be understood and calculated.

Conclusion

In summary, resistors in parallel do not add up the voltage; they see the same voltage as the source. The confusion arises when the total current, which is the sum of the individual currents, is considered. In parallel circuits, the focus is on the voltage across each resistor being the same, while in series circuits, it is on the sum of the voltages.

Key Takeaways

Parallel resistors see the same voltage as the source. Series resistors have their voltages summed up. The total voltage in a parallel circuit is the same across all branches. The total current in a parallel circuit is the sum of the currents through each branch.

Related Keywords

Parallel resistors, voltage division, electrical circuits, series voltage addition, identical resistors

References

[1] "Parallel Resistors," Wikipedia

[2] Electronics Tutorials

[3] Hyper Physics