In a parallel circuit, what is the expected effect on the total resistance if all resistors are of equal value and one is removed?

In a parallel circuit, the total resistance is determined by the reciprocal of the sum of the reciprocals of each individual resistor's resistance. When all resistors are of equal value, the formula for the total resistance becomes:

1/R_total = 1/R + 1/R + ... + 1/R (for the number of resistors, n).

This simplifies to:

R_total = R/n, where R is the resistance of one resistor, and n is the number of resistors.

If one resistor is removed from this parallel configuration, the total number of resistors decreases from n to n-1. Therefore, the new total resistance can be computed as:

R_new_total = R/(n-1).

As the value of n decreases, the denominator (n - 1) becomes smaller, resulting in a larger value for R_new_total compared to R_total. Hence, the total resistance increases when a resistor is removed from one of all equal value in a parallel circuit. This is because, with fewer pathways for current to flow, the overall ability for the circuit to conduct electricity diminishes, leading to a higher total resistance. Thus, the correct response reflects this understanding of how parallel circuits behave when resistive components are removed.