Find resistance from measured current: Twelve volts are applied across an unknown resistor and the measured current is 3 mA. What is the resistor value?

Introduction / Context:
Translating a measured current into a resistance value is a core diagnostic skill. It is especially helpful when checking unknown components or verifying that a circuit behaves as designed at low currents.

Given Data / Assumptions:

• Applied voltage V = 12 V.
• Measured current I = 3 mA = 0.003 A.
• Assume ideal resistor behaviour; DC conditions.

Concept / Approach:
Rearrange Ohm’s law to R = V / I. Expect a kilo-ohm range because tens of volts divided by milliamps yields thousands of ohms. Meticulous unit conversion prevents large errors.

Step-by-Step Solution:

Verification / Alternative check:
Back compute the current using 4 kΩ: I = 12 / 4000 = 0.003 A = 3 mA, which reproduces the measured value exactly. Power check: P = V * I = 12 * 0.003 = 0.036 W, so a 0.125 W or 0.25 W resistor is more than sufficient.

Why Other Options Are Wrong:

• 4 Ω or 4.4 Ω: Would allow multi-ampere currents at 12 V.
• 400 Ω: Would yield I = 12 / 400 = 30 mA, ten times higher than measured.

Common Pitfalls:

• Dropping the milli prefix in current, leading to 400 Ω instead of 4 kΩ.
• Confusing kΩ with Ω when reading options quickly.

Final Answer:
4 kΩ