Parallel Resistor

Definition

A parallel resistor is a resistor that is connected alongside one or more resistors in an electrical circuit, allowing multiple pathways for current to flow. This configuration decreases the overall resistance of the circuit and increases the total current that can flow through it. When resistors are arranged in parallel, the voltage across each resistor remains the same, which is crucial for understanding how they work together in a circuit.

5 Must Know Facts For Your Next Test

1. In a parallel resistor circuit, the total resistance can be calculated using the formula $$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}$$, where $$R_1, R_2,..., R_n$$ are the individual resistances.
2. Adding more resistors in parallel will always decrease the total resistance of the circuit, making it easier for current to flow.
3. The current through each parallel resistor can be different, depending on their individual resistances; however, the total current is the sum of these individual currents.
4. If one of the resistors in a parallel circuit fails (opens), current will still flow through the remaining resistors, allowing the circuit to continue functioning.
5. Parallel resistor configurations are commonly found in electrical devices and systems where multiple components need to operate independently while sharing a common voltage supply.

Review Questions

• How does connecting resistors in parallel affect the total resistance and current in an electrical circuit?
  • Connecting resistors in parallel lowers the total resistance of the circuit because there are multiple pathways for current to flow. This configuration allows more total current to pass through than if they were connected in series. The formula $$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$$ illustrates how adding additional resistors decreases overall resistance. Each resistor experiences the same voltage drop across it, but they can carry different amounts of current based on their individual resistances.
• Describe how you would calculate the equivalent resistance of three resistors connected in parallel with values of 4Ω, 6Ω, and 12Ω.
  • To calculate the equivalent resistance for three resistors in parallel, use the formula $$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$. For this case: $$\frac{1}{R_{total}} = \frac{1}{4} + \frac{1}{6} + \frac{1}{12}$$. Finding a common denominator (which is 12) gives: $$\frac{3}{12} + \frac{2}{12} + \frac{1}{12} = \frac{6}{12}$$. Thus, $$R_{total} = 2Ω$$. This shows how adding these resistors in parallel effectively reduces total resistance to 2Ω.
• Evaluate how a change in one resistor's value in a parallel configuration affects the overall circuit behavior and performance.
  • Changing one resistor's value in a parallel configuration directly affects both the equivalent resistance and current distribution among all resistors. For instance, if you decrease one resistor's value significantly, it will draw more current due to its lower resistance compared to others. This change can lead to increased overall current from the power source while reducing total resistance further. If that resistor fails, the remaining resistors still provide pathways for current flow, demonstrating resilience. Understanding these relationships is crucial for designing circuits that must maintain performance despite component variations.

Related terms

Total Resistance:

The combined resistance of two or more resistors in a circuit, calculated differently depending on whether the resistors are in series or parallel.

Ohm's Law:

A fundamental relationship in electrical circuits that states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance.

Voltage Divider:

A simple circuit configuration using resistors to create a specific voltage output from a higher voltage source, often used to obtain reference voltages.