Parallel Resistor

Definition

A parallel resistor is a resistor configuration in which two or more resistors are connected across the same two nodes, providing multiple paths for current to flow. This setup results in a combined resistance that is lower than the smallest individual resistance and allows for the distribution of total current among all connected resistors, significantly impacting circuit behavior and analysis.

5 Must Know Facts For Your Next Test

1. In a parallel resistor configuration, the voltage across each resistor is the same, allowing for an equal share of voltage regardless of their individual resistance values.
2. The formula for calculating equivalent resistance for resistors in parallel is given by $$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}$$.
3. Adding more resistors in parallel decreases the overall resistance, which can increase total current flow from the power source according to Ohm's Law.
4. If one resistor in a parallel configuration fails (becomes open), the remaining resistors will still carry current, allowing the circuit to function.
5. Parallel resistors are commonly used in applications where current needs to be shared, such as in load balancing or redundancy in electrical systems.

Review Questions

• How does connecting resistors in parallel affect the total current flowing through a circuit?
  • Connecting resistors in parallel increases the total current flowing through the circuit. This happens because each resistor provides an additional path for current to flow, leading to a decrease in overall resistance. According to Ohm's Law, as resistance decreases while voltage remains constant, total current must increase, allowing for more efficient power distribution across multiple components.
• Explain how to calculate the equivalent resistance of three resistors connected in parallel with values of 4Ω, 6Ω, and 12Ω.
  • To calculate the equivalent resistance of three resistors connected in parallel, you use the formula $$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$. Plugging in the values gives $$\frac{1}{R_{eq}} = \frac{1}{4} + \frac{1}{6} + \frac{1}{12}$$. Finding a common denominator (which is 12), we convert each fraction: $$\frac{3}{12} + \frac{2}{12} + \frac{1}{12} = \frac{6}{12}$$. Therefore, $$R_{eq} = 2Ω$$.
• Analyze how a failure in one of several parallel resistors affects circuit functionality and overall performance.
  • When one of several parallel resistors fails by becoming an open circuit, it does not prevent current from flowing through the remaining resistors. This redundancy allows the circuit to continue functioning, albeit with altered performance. The overall equivalent resistance increases due to fewer paths for current flow, potentially resulting in decreased total current supplied by the source. However, this design enhances reliability since failure of one component does not compromise the entire circuit.

Related terms

Equivalent Resistance:

The total resistance of a circuit that combines multiple resistors into a single resistor that has the same effect on current flow.

Voltage Divider:

A configuration of resistors arranged in series that divides the input voltage into smaller output voltages based on the resistor values.

Ohm's Law:

A fundamental principle stating that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance.