Finding each resistor from total series resistance: Five equal resistors are in series with a 20 V DC source. The measured circuit current is 400 µA. What is the resistance of each individual resistor?

Introduction / Context:When equal resistors are in series, the total resistance is simply N times one resistor’s value. Measuring the current with a known source quickly yields total resistance, and division by N gives each individual resistance. This is a standard application of Ohm’s law and series rules.

Given Data / Assumptions:

• Number of equal resistors N = 5 in series.
• Source voltage V = 20 V DC.
• Measured current I = 400 µA = 0.0004 A.

Concept / Approach:Ohm’s law: R_total = V / I. For equal series parts, R_each = R_total / N. Unit handling is critical: microampere to ampere conversion must be correct to avoid a 10^6 error factor.

Step-by-Step Solution:

Verification / Alternative check:Reverse-calculate current using R_each = 10 kΩ: total is 5 * 10 kΩ = 50 kΩ; I = 20 / 50,000 = 0.0004 A = 400 µA. Match confirmed.

Why Other Options Are Wrong:50 kΩ is the total, not each. 125 Ω and 20 Ω are far too small; they would produce much larger currents. 2 kΩ would make the total 10 kΩ, implying 2 mA, not the given 400 µA.

Common Pitfalls:Forgetting to convert microamperes to amperes; using parallel formulas instead of series addition for equal parts.

Final Answer:10 kΩ