Finding unknown parallel resistors: Two resistors are connected in parallel with total equivalent resistance RT = 8 Ω. One resistor has double the resistance of the other. What are the individual resistor values?

Introduction / Context:
Determining branch values from the equivalent parallel resistance is a classic algebraic exercise. It appears when replacing networks with standard part values or diagnosing mismatched components.

Given Data / Assumptions:

• Two unknown resistors in parallel.
• RT = 8 Ω.
• One resistor is exactly double the other.

Concept / Approach:
Let the smaller resistor be R and the larger be 2R. For two resistors in parallel, RT = (R * 2R) / (R + 2R) = (2R^2) / (3R) = (2/3) R. Solve algebraically for R, then list both values.

Step-by-Step Solution:
Set 8 = (2/3) R.Solve for R: R = 8 * 3 / 2 = 12 Ω.Therefore, the other resistor is 2R = 24 Ω.

Verification / Alternative check:
Compute equivalent: (12 * 24) / (12 + 24) = 288 / 36 = 8 Ω. Checks out exactly.

Why Other Options Are Wrong:
Other pairs do not satisfy both conditions (parallel equivalent of 8 Ω and a 2:1 ratio). For instance, 10 Ω and 20 Ω in parallel yield 6.67 Ω, not 8 Ω.

Common Pitfalls:
Using series formulas or mixing up which number is larger (the 2R must exceed R).

Final Answer:
12 Ω and 24 Ω