The correct option is Decrease the equivalent resistance.
Explanation
In electrical circuits, resistors can be connected in series or parallel. In a parallel combination, components are connected across the same potential difference, providing multiple distinct paths for current to flow. The equivalent resistance ($R_{eq}$) of a parallel network is calculated using the reciprocal formula:
$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}$
Analysis:
- Conductance and Resistance: The reciprocal of resistance is known as conductance ($G = \frac{1}{R}$). In a parallel circuit, the total conductance is the sum of the individual conductances of each branch.
- Effect of Adding a Branch: When an additional finite-resistance branch is added to a parallel combination, a positive term is added to the sum of conductances. This increases the total conductance of the circuit.
- Result on Equivalent Resistance: Since resistance is the inverse of conductance, an increase in total conductance mathematically results in a decrease in total equivalent resistance.
- Physical Interpretation: Physically, adding a parallel branch creates an extra path for charge carriers to move through. This reduces the overall restriction (resistance) to the flow of current from the voltage source. Consequently, the equivalent resistance of a parallel combination is always lower than the smallest individual resistance in the network.
Key Takeaway:
Adding a resistor in parallel always decreases the equivalent resistance of the circuit because it provides an additional path for current flow, thereby increasing the total conductance.