Unit conversion in electrical measurements: How many microamperes (µA) are in 2 milliamperes (mA)?
-
A2 µA
-
B20 µA
-
C200 µA
-
D2,000 µA
Answer
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