If one resistor is removed from a parallel circuit, what happens to the total resistance of the circuit?

When one resistor is removed from a parallel circuit, the total resistance of the circuit increases. This can be understood through the nature of how resistors function in parallel. The total resistance (R_t) for resistors in parallel is calculated using the formula:

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

When a resistor is removed, the total number of resistors in the equation decreases, which means that the sum of the reciprocal of the resistances becomes smaller. As a result, the total resistance (R_t) increases.

In practical terms, removing a resistor from a parallel circuit reduces the pathways available for current to flow, thereby making it more difficult for current to pass through the circuit. When there are fewer paths for the current, overall resistance of the circuit rises, leading to a higher total resistance. This aligns with the principle that adding more resistors in parallel lowers the total resistance, while removing them does the opposite.