How does the number of electrical resistors in parallel affect the total resistance in the circuit?

The total resistance in a parallel circuit behaves uniquely due to the nature of how resistors are arranged. When resistors are connected in parallel, each additional resistor provides an alternative path for current to flow. This structure effectively increases the overall capacity of the circuit to conduct electricity, which results in a decrease in total resistance.

Mathematically, the total resistance ( R_t ) in a parallel circuit can be calculated using the formula:

[

\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots

]

As more resistors are added, the sum of the reciprocals increases, which in turn decreases the total resistance ( R_t ). This means that as the number of resistors in parallel increases, the total resistance will continue to drop, allowing for more current to flow through the circuit. Therefore, the correct understanding is that total resistance decreases as the number of resistors increases.