Four identical resistors in parallel draw 2 mA total at 10 V: What is the resistance value of each individual resistor?

Introduction / Context:When equal resistors are paralleled, the equivalent resistance scales simply with the number of branches. This problem combines Ohm's law with equal-parallel relationships to recover individual resistance from total current and voltage.

Given Data / Assumptions:

• Total source voltage: 10 V.
• Total source current: 2 mA = 0.002 A.
• Number of equal branches: 4.

Concept / Approach:First compute total equivalent resistance R_eq = V / I. For N equal resistors of value R in parallel, R_eq = R / N → R = N * R_eq. Convert the final result to kΩ where appropriate.

Step-by-Step Solution:

Verification / Alternative check:If each branch is 20 kΩ, branch current I_b = 10 / 20,000 = 0.0005 A = 0.5 mA. Total current for 4 branches = 4 * 0.5 mA = 2 mA, matching the given data.

Why Other Options Are Wrong:

• 12.5 Ω, 50 Ω, 200 Ω: Far too small; would draw much larger total current at 10 V.

Common Pitfalls:

• Inverting the relationship (using R = R_eq / N instead of R = N * R_eq for equal parallel resistors).
• Forgetting to convert between mA and A, leading to a 1,000× error.

Final Answer:20 kΩ