Compute the equivalent resistance for resistors in parallel What is the total resistance RT of 12 kΩ, 4 kΩ, and 3 kΩ connected in parallel?

Introduction / Context:
Calculating equivalent resistance of parallel resistors is a routine but critical task in electronics. It determines load seen by sources, affects current sharing, and impacts power dissipation and noise performance in analog designs.

Given Data / Assumptions:

• Three resistors: R1 = 12 kΩ, R2 = 4 kΩ, R3 = 3 kΩ.
• All three are connected in parallel across the same two nodes.
• DC conditions and ideal components.

Concept / Approach:
For resistors in parallel, conductances add: 1/RT = 1/R1 + 1/R2 + 1/R3. After summing the reciprocals, invert to get RT. Using kilohm units throughout avoids unit mistakes.

Step-by-Step Solution:

Verification / Alternative check:
Use pairwise combination: combine 3 kΩ || 6 kΩ (since 12 kΩ || 4 kΩ = 3 kΩ) gives 3 kΩ || 3 kΩ = 1.5 kΩ. Both methods agree.

Why Other Options Are Wrong:

• 2 kΩ: corresponds to 1/RT = 0.5 kΩ^-1, which is smaller than the actual sum of conductances.
• 6.3 kΩ or 19 kΩ: larger than the smallest branch resistance; a parallel equivalent can never exceed the smallest resistor.

Common Pitfalls:
Failing to keep consistent units (ohms vs kilohms) and forgetting that the equivalent of parallel resistors is always less than the smallest individual resistor.

Final Answer:
1.5 kΩ