Repair for solvability — two resistors of 12 kΩ and 8 kΩ are connected in parallel. What is the total (equivalent) resistance of the circuit?

Introduction / Context:When resistors are in parallel, their equivalent resistance is less than the smallest branch resistance. Calculating with the reciprocal formula gives precise values used in design checks.

Given Data / Assumptions:

• R1 = 12 kΩ, R2 = 8 kΩ, connected in parallel.
• Ideal resistors and wiring.

Concept / Approach:Use the parallel formula: 1/Req = 1/R1 + 1/R2. For two branches it is often convenient to use the product-over-sum shortcut: Req = (R1 * R2) / (R1 + R2).

Step-by-Step Solution:

Verification / Alternative check:Reciprocal method: 1/Req = 1/12 + 1/8 = 0.0833 + 0.125 = 0.2083 (1/kΩ) → Req ≈ 4.8 kΩ.

Why Other Options Are Wrong:

Common Pitfalls:Adding resistances directly (series rule) instead of using reciprocal sum for parallel.

Final Answer:4.8 kΩ