Two-resistor parallel solver: The total parallel resistance is 1,403 Ω and one branch is 2 kΩ. What is the value of the other resistor?

Introduction / Context:
Determining an unknown parallel branch from the known total and one branch is a common troubleshooting task. Using the reciprocal form of the parallel resistance formula avoids trial-and-error and gives a quick, exact value.

Given Data / Assumptions:

• Total resistance, R_T = 1,403 Ω.
• Known branch, R1 = 2,000 Ω.
• Unknown branch, R2 = ?
• Only two branches are present.

Concept / Approach:

For two resistors in parallel, 1/R_T = 1/R1 + 1/R2. Solve for 1/R2 = 1/R_T − 1/R1, then invert to get R2. Keep units consistent in ohms to prevent scaling errors.

Step-by-Step Solution:

Verification / Alternative check:

Cross-check with product-over-sum shortcut: R_T = (R1 * R2)/(R1 + R2). Insert R2 = 4.7 kΩ and verify ≈ 1,403 Ω.

Why Other Options Are Wrong:

1,403 Ω is the total, not a branch. 2 kΩ is the known branch. 3,403 Ω does not satisfy the parallel equation with the given total.

Common Pitfalls:

Arithmetic errors in reciprocals; forgetting to invert at the end; mixing kΩ and Ω without conversion.

Final Answer:

4.7 kΩ