Which of the following is correct concerning a parallel circuit?

• A. Total resistance will be smaller than the smallest resistor.
• B. Total resistance will decrease when one of the resistances is removed.
• C. Total voltage drop is the same as the total resistance.
• D. Total current is greater than the sum of the branch currents.

Answer: (A)

In a parallel circuit, multiple paths for current mean the currents can split among the branches, while the voltage across each branch is the same as the source. Because currents can take several routes, the total or equivalent resistance is less than any one of the individual resistors. This is captured by 1/R_eq = 1/R1 + 1/R2 + ..., so R_eq is always smaller than the smallest resistor.

That’s why the total resistance being smaller than the smallest resistor is the correct statement. For example, two resistors of 4 ohms each in parallel give an equivalent of 2 ohms, which is smaller than either resistor.

The other ideas don’t fit parallel behavior. Removing a resistor from a parallel network reduces the number of paths, causing the total resistance to increase, not decrease. The total voltage drop in a parallel circuit is the same as the source voltage across every branch, but it isn’t a direct comparison to the total resistance. And the total current entering a parallel network equals the sum of the currents in each branch, not greater than that sum.