NEIEP Mechanics Practice Exam

What is true about total resistance in a parallel circuit?

1. Always greater than any one branch

2. Equal to the total of all branch resistances

3. Always less than the resistance of any one branch

4. Cannot be calculated

The correct answer is: Always less than the resistance of any one branch

In a parallel circuit, the total resistance is indeed always less than the resistance of any single branch. This occurs because in a parallel configuration, multiple paths are created for the current to flow. Each branch provides an alternative route, and since current can split across these paths, it effectively reduces the total resistance experienced by the circuit. Mathematically, the total resistance in a parallel circuit (R_total) can be calculated using the formula: 1/R_total = 1/R_1 + 1/R_2 + 1/R_3 + ... Where R_1, R_2, R_3, etc., are the resistances of the individual branches. As the number of branches increases or as the resistance of each branch decreases, the total resistance approaches zero, which illustrates how it can be lower than that of any single branch. Understanding this principle is essential because it helps in analyzing circuit behavior, calculating current distribution, and ensuring the effective design of electrical systems. Thus, stating that the total resistance in a parallel circuit is always less than the resistance of any one branch is accurate and reflects the fundamental law of parallel resistances.