Final answer:
The total resistance for the resistors connected in series is 6600 ohms. For the parallel connection, the equivalent resistance is approximately 88.1 ohms.
Step-by-step explanation:
Calculating Series and Parallel Resistances
To find the total resistance of resistors connected in series, you add their resistances together. For the given resistors of 1.00 × 10² ohms (100 ohms), 2.50 kΩ (2500 ohms), and 4.00 kΩ (4000 ohms), the total series resistance is the sum of all these values, which is 100 ohms + 2500 ohms + 4000 ohms = 6600 ohms or 6.6 kΩ.
For parallel resistors, the equivalent resistance is found by using the formula 1/R_eq = 1/R_1 + 1/R_2 + 1/R_3. So for the resistors mentioned, the equivalent resistance in parallel would be calculated as follows: 1/R_eq = 1/100 + 1/2500 + 1/4000, which results in an equivalent resistance R_eq of approximately 88.1 ohms.
Therefore, the correct answer is: (a) 6600 ohms in series and (b) 88.1 ohms in parallel.