Understanding Parallel Resistors: Voltage and Current Characteristics

When resistors are wired in parallel, a unique set of electrical characteristics emerges. This article delves into the key properties that must be the same and those that can differ, all in the context of understanding electrical circuits more deeply.

Introduction to Parallel Resistor Circuits

In an electrical circuit, resistors can be arranged in series or in parallel. When resistors are arranged in parallel, they share a common node on one side and another common node on the other side. This arrangement affects how voltage and current behave across and through the resistors.

The Same: Voltage Across Each Resistor

One of the key characteristics of parallel resistors is that the voltage across each resistor must be the same. This is a fundamental principle in electrical circuits, and it is vital for understanding the behavior of parallel circuits.

Mathematically, if you apply the same voltage to each parallel resistor, the voltage drop across each resistor will be identical. This can be expressed as:

Where Veq is the voltage across each resistor, and VR1 and VR2 are the voltages across resistors R1 and R2, respectively.

The Same: Current through Resistors (With Special Cases)

Contrary to the voltage, the current through parallel resistors is not necessarily the same for each resistor. The current through each resistor depends on its resistance value. If the two resistors are identical, the current will be the same through both of them. However, for resistors with different values, the current through each will be different. The current through a resistor can be calculated using Ohm's Law:

IR VR / R

Where IR is the current through the resistor, VR is the voltage across the resistor, and R is the resistance of the resistor.

Equivalent Resistance of Parallel Connectors

To understand the total resistance seen by the circuit, we need to calculate the equivalent resistance (Req) of the parallel resistors. If two resistors R1 and R2 are connected in parallel, the formula to calculate their equivalent resistance is:

1/Req 1/R1 1/R2

Solving for Req, we get:

Req R1R2 / (R1 R2)

This formula demonstrates that the equivalent resistance of parallel resistors is always lower than the lowest individual resistor value.

Power Dissipation in Parallel Resistors

The power dissipated by each resistor in a parallel circuit is determined by the product of the voltage across it and the current through it. The power dissipated by a resistor R in a parallel circuit can be calculated using the formula:

P V2 / R

or

P I2 R

Rearranging the formula to find the power in a parallel resistor, we get:

P V 2 / R for a given voltage,

P (VR / R) VR for a given current through the resistor.

Conclusion

In summary, when resistors are connected in parallel, the voltage across each resistor must be the same, but the current through each resistor can differ based on their resistance values. Understanding these principles is crucial for working with parallel circuits and designing electronic systems effectively.