In a parallel circuit, when you remove a resistor, the total resistance of the circuit will increase. This is because parallel resistors provide additional pathways for current to flow; removing one of those pathways means that there are fewer options for the current to flow through.
The total resistance \( R_t \) of resistors in parallel can be 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 overall equivalent resistance increases because the reciprocal of the total resistance depends on the number of resistors in the circuit. Fewer resistors in parallel lead to a larger equivalent resistance. Thus, the total resistance of the circuit will rise when a resistor is removed.