Adding a branch in parallel: When an additional resistor is connected across an existing parallel network, what happens to the total resistance?

Introduction / Context:
Parallel networks reduce equivalent resistance by providing multiple current paths. Understanding how total resistance changes when you add or remove branches is fundamental for designing dividers, loads, and input networks.

Given Data / Assumptions:

• An existing parallel circuit with some equivalent resistance R_eq.
• One more resistor branch is added in parallel.
• All elements are ideal; source voltage remains constant.

Concept / Approach:

Parallel combination rule: 1 / R_new = 1 / R_eq + 1 / R_added. Because 1 / R_added is positive, the reciprocal sum increases, making R_new smaller than R_eq. Therefore, adding any finite positive resistance in parallel decreases the total resistance.

Step-by-Step Solution:

Verification / Alternative check:

Numerical example: R_eq = 100 Ω, R_added = 100 Ω gives R_new = 50 Ω. The trend holds for all finite positive resistances added in parallel.

Why Other Options Are Wrong:

'Remains the same' would require an infinite added resistance (open circuit), not a real resistor. 'Increases' or arithmetic adjustments by the resistor value apply to series, not parallel, combinations.

Common Pitfalls:

Confusing series and parallel effects; trying to add resistances directly in a parallel network.

Final Answer:

decreases