Unit conversion in electrical measurements: How many microamperes (µA) are in 2 milliamperes (mA)?

Difficulty: Easy

Correct Answer: 2,000 µA

Explanation:


Introduction / Context:
Accurate unit conversion is fundamental in circuit analysis, instrumentation, and troubleshooting. Small mistakes with metric prefixes (milli, micro, nano) can lead to errors by factors of 10^3 or more. This item reinforces the relationship between milliamperes and microamperes in SI units.


Given Data / Assumptions:

  • 1 A is the base SI unit of electric current.
  • Milli- (m) denotes 10^-3.
  • Micro- (µ) denotes 10^-6.
  • We need to convert 2 mA into µA.


Concept / Approach:
Express both given and target units as powers of ten relative to amperes, then divide or multiply to convert. Alternatively, use the ratio 1 mA = 1000 µA derived from 10^-3 A vs 10^-6 A (difference of 10^3).


Step-by-Step Solution:

Write 2 mA in amperes: 2 mA = 2 * 10^-3 A.Convert amperes to microamperes: 1 µA = 10^-6 A → 1 A = 10^6 µA.Compute: 2 * 10^-3 A = 2 * 10^-3 * 10^6 µA = 2 * 10^3 µA = 2000 µA.


Verification / Alternative check:
Use the known shortcut: 1 mA = 1000 µA. Therefore, 2 mA = 2 * 1000 µA = 2000 µA. Both methods agree.


Why Other Options Are Wrong:

  • 2 µA: Off by 10^3; confuses milli with micro.
  • 20 µA: Off by 10^2; still confuses prefixes.
  • 200 µA: Off by 10; incorrect scaling.


Common Pitfalls:

  • Mixing up 'm' (milli, 10^-3) and 'µ' (micro, 10^-6).
  • Forgetting to reconcile powers of ten when chaining conversions.


Final Answer:
2,000 µA

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