Perform submultiples conversion: convert 7,000 nA (nanoamperes) into microamperes (µA) and select the correct value.
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A0.007 µA
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B0.7 µA
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C700 µA
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D7 µA
Answer
Correct Answer: 7 µA
Explanation
Introduction / Context:Working with small currents requires comfort with SI prefixes. Nano (n) and micro (µ) are ubiquitous in sensor circuits, leakage measurements, and low-power design. This problem reinforces the 1000:1 relationship between adjacent prefixes.
Given Data / Assumptions:
- Given value: 7,000 nA.
- 1 µA = 1,000 nA.
- Goal: express in µA.
Concept / Approach:
To convert from nano to micro, divide by 1,000 because micro is the next larger step: 10^-6 vs 10^-9. In exponential form, 7,000 × 10^-9 A becomes 7,000 × 10^-9 A = 7 × 10^-6 A = 7 µA.
Step-by-Step Solution:
Write 7,000 nA as 7,000 × 10^-9 A.Group: 7,000 × 10^-9 = 7 × 10^3 × 10^-9 = 7 × 10^-6 A.Recognize 10^-6 A as µA → 7 µA.Verification / Alternative check:
Unit-ladder method: nA → µA is ÷ 1000, so 7,000 ÷ 1000 = 7 µA. Both methods agree.
Why Other Options Are Wrong:
0.007 µA and 0.7 µA are off by 1000× and 10× respectively; 700 µA is off by 100× in the other direction.
Common Pitfalls:
Multiplying instead of dividing when moving to a larger prefix; misreading µ (micro) as m (milli).
Final Answer:
7 µA