Question

in a parallel circuit, adding more branches provides more pathways for current to flow, which ____ the overall resistance to current flow; thus, current flow ____. select one: a. decreases; decreases b. increases; increases c. decreases; increases d. increases; decreases

Explanation:

Step1: Recall the formula for parallel resistance

The formula for equivalent resistance \(R_{eq}\) in a parallel circuit with resistors \(R_1,R_2,\cdots,R_n\) is \(\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\cdots+\frac{1}{R_n}\). When more branches (resistors) are added, \(\frac{1}{R_{eq}}\) increases (since we are adding positive terms \(\frac{1}{R_i}\)), so \(R_{eq}\) decreases.

Step2: Use Ohm's law \(I = \frac{V}{R}\)

Assuming the voltage \(V\) across the parallel - circuit (from the power source) is constant. Since \(I=\frac{V}{R}\), when \(R = R_{eq}\) decreases (as shown in Step 1), and \(V\) is constant, the current \(I\) (current flow) increases.

So, adding more branches decreases the overall resistance and increases the current flow.

Answer:

C. Decreases; increases