Difficulty: Medium
Correct Answer: 384 kΩ
Explanation:
Introduction / Context:
This problem applies Ohm's law and series-resistance addition to determine an unknown resistor in a series string given the total current and supply voltage. Such calculations are common in sensor ladders, bias networks, and precision dividers where one element value must be chosen to meet a target current.
Given Data / Assumptions:
Concept / Approach:
In series, total resistance is the sum of individual resistances. Ohm's law gives R_total = Vs / I_total. The unknown is R4 = R_total - (R1 + R2 + R3). Careful unit conversion (kΩ to Ω, µA to A) avoids arithmetic errors.
Step-by-Step Solution:
Compute total resistance: R_total = Vs / I_total = 50 V / (100 * 10^-6 A).R_total = 50 / 0.0001 = 500,000 Ω = 500 kΩ.Sum known resistors: R_known = 12 kΩ + 47 kΩ + 57 kΩ = 116 kΩ.Find the unknown: R4 = R_total - R_known = 500 kΩ - 116 kΩ = 384 kΩ.Therefore, R4 = 384 kΩ.
Verification / Alternative check:
Check current with the found value: R_sum = 116 kΩ + 384 kΩ = 500 kΩ. Then I = Vs / R_sum = 50 V / 500 kΩ = 0.0001 A = 100 µA, which matches the given current. The result is self-consistent.
Why Other Options Are Wrong:
Common Pitfalls:
Final Answer:
384 kΩ
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