Final answer:
The total resistance of a 100 ohms, a 2.50 kilohms, and a 4.00 kilohms resistor connected in series is 6.60 kohms, while in parallel it is approximately 93.90 ohms.
Step-by-step explanation:
To calculate the total resistance of resistors in series, simply add the resistance values of each resistor. In parallel, the total resistance is found using the reciprocal of the sum of the reciprocals of each individual resistance.
Series: For resistors in series, the total resistance (Rtotal) is the sum of the resistances:
Rtotal = R1 + R2 + R3
Given resistances:
100 ohms (1.00 × 102 ohms),
2.50 kilohms (2.50 kohms),
4.00 kilohms (4.00 kohms)
Total resistance in series:
Rtotal = 100 ohms + 2,500 ohms + 4,000 ohms = 6,600 ohms or 6.60 kohms
Parallel: For resistors in parallel, use the formula:
1 / Rtotal = 1 / R1 + 1 / R2 + 1 / R3
To calculate the total resistance in parallel:
- Convert all resistances to ohms.
- Compute the reciprocal for each resistance.
- Add all the reciprocals together.
- Take the reciprocal of the sum for the total resistance in parallel.
Total resistance in parallel:
1 / Rtotal = 1 / 100 + 1 / 2500 + 1 / 4000
Rtotal = 1 / (0.01 + 0.0004 + 0.00025) = 1 / 0.01065 ≈ 93.90 ohms