Master the Basics: Understanding Resistors in Parallel

Resistors are connected in parallel when both of their terminals are connected to each terminal of another resistor. This configuration decreases the total resistance, as it provides more paths for current to flow. Let’s explore how resistors in parallel work and how to calculate their total resistance.

How Do Resistors in Parallel Work?

Think of current passing through a resistor like cars traveling down a road:

• Adding a second resistor in parallel creates an additional path for the cars to travel.
• The resistance along each path corresponds to the difficulty of traveling it (e.g., potholes represent higher resistance).

When multiple resistors are connected in parallel, the total resistance is reduced because the current splits among the available paths. For example:

• Two equal resistors in parallel halve the total resistance.
• Three equal resistors in parallel reduce the total resistance to one-third of a single resistor's value.

Calculating Resistance in Parallel

For resistors of equal value, the total resistance is:

Total Resistance = Individual Resistance / Number of Resistors

For resistors with different values, use the following formula:

1 / Rtotal = 1 / R1 + 1 / R2 + ...

Example: Two Resistors with Different Values

Consider a 10 kΩ resistor and a 20 kΩ resistor in parallel:

1. Calculate the reciprocals of the resistances:
• 1 / 10 kΩ = 0.0001
• 1 / 20 kΩ = 0.00005
2. Add the reciprocals: 0.0001 + 0.00005 = 0.00015
3. Take the reciprocal of the result to find the total resistance:
• R_total = 1 / 0.00015 ≈ 6.66 kΩ

Practical Demonstration

Using a breadboard, you can measure the resistance of parallel resistors:

• Combine a 10 kΩ resistor with a 20 kΩ resistor (created by placing two 10 kΩ resistors in series).

• Measure the total resistance using a digital multimeter (DMM). The result should be approximately 6.6 kΩ.

Current and Power Distribution

When resistors are connected in parallel, current and power are distributed based on their resistance values:

1. Total Current: Using Ohm's Law (I = V / R), a 5V source across a total resistance of 6.66 kΩ will draw 0.75 mA of current.
2. Individual Currents:
• 10 kΩ resistor: 5V / 10 kΩ = 0.5 mA
• 20 kΩ resistor: 5V / 20 kΩ = 0.25 mA
3. These currents add up to the total current: 0.5 mA + 0.25 mA = 0.75 mA.
4. Power Dissipation:
• 10 kΩ resistor: P = IV = 0.5 mA × 5V = 2.5 mW
• 20 kΩ resistor: P = IV = 0.25 mA × 5V = 1.25 mW

The total power dissipated is 2.5 mW + 1.25 mW = 3.75 mW, matching the earlier calculation.

Key Takeaways

• Resistors in parallel reduce total resistance, providing more paths for current to flow.
• For equal resistors, divide the resistance by the number of resistors.
• For unequal resistors, use the reciprocal formula to calculate total resistance.
• Current and power are distributed based on the resistance values of each path.

Understanding resistors in parallel is crucial for designing and analyzing circuits. Practice these calculations to build a solid foundation for more complex electronics projects!