Final answer:
The total resistance in a parallel circuit with 10-ohm, 20-ohm, 100-ohm, and 200-ohm resistors is found using the reciprocal formula, resulting in approximately 6.06 ohms, which is not one of the provided options.
Step-by-step explanation:
Finding Total Resistance in a Parallel Circuit
To find the total resistance in a parallel circuit with resistors of different values, you use the reciprocal formula:
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn. Applying this formula to the given circuit with resistors of 10 ohms, 20 ohms, 100 ohms, and 200 ohms gives:
- Calculate the reciprocal of each resistance: 1/10 + 1/20 + 1/100 + 1/200.
- Perform the addition: this becomes 0.1 + 0.05 + 0.01 + 0.005 = 0.165.
- Find the reciprocal of the sum to get the equivalent resistance: 1/0.165 = 6.06 (approximately).
None of the answer choices a) 100 ohms, b) 200 ohms, c) 500 ohms, or d) 400 ohms is correct. Thus, the total resistance of the parallel circuit is approximately 6.06 ohms.