Final answer:
The resistance across terminals a and b with a single 25 ohm resistor connected is 25 ohms. In a series circuit, total resistance is the sum of individual resistances while in parallel, the equivalent resistance is less than the smallest individual resistance and calculated using reciprocals.
Step-by-step explanation:
If a 25 ohm resistor is connected across terminals a and b, the resistance across these terminals is simply the resistance of the single resistor, hence the equivalent resistance is 25 ohms. When resistors are connected in series, their resistances add up, so for instance, a 1.00 × 10² -2, a 2.50-kΩ, and a 4.00-kΩ resistor in series will have a total resistance of the sum of the three resistances. For resistors in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of each resistor's resistance, which results in a lower equivalent resistance compared to any individual resistance in the circuit.
For a circuit of parallel resistors with the smallest resistor being 25 ohms, the upper limit of the equivalent resistance will be 25 ohms, because no matter how many resistors are added in parallel, the equivalent resistance will not exceed the smallest individual resistor's resistance.
When dealing with multiple resistors in a circuit, calculating the equivalent resistance depends on whether they are connected in series or in parallel, and applying the corresponding formulas for each case.