Units, scale, and estimates

• Convert units, preserve dimensions through a calculation, and make a bounded estimate that can eliminate an implausible design choice.

No prerequisites are listed.

A number without a unit is rarely a useful engineering statement. “The fan needs 3” could mean 3 volts, 3 amperes, or 3 watts, each implying a different build. Units behave like algebraic factors: 250 mA is 0.250 A, and multiplying 5 V by 0.250 A gives 1.25 V·A, called watts for DC power. Prefixes encode powers of ten: milli is 10^-3, micro is 10^-6, and kilo is 10^3. Writing conversions as fractions whose equal quantities cancel—250 mA × (1 A / 1000 mA)—makes mistakes visible.

Dimensions describe the kind of quantity independently of the chosen unit. Speed has dimension length/time, so a proposed expression for speed must reduce to that form. Dimensional agreement cannot prove an equation is correct, but disagreement proves it is wrong. Scale adds another filter. Before selecting a battery for a small blower, estimate power from rated voltage and current, operating time from energy divided by power, then include a loss margin. A one-significant-figure estimate is often enough to reject a coin cell and move toward a suitable protected pack.

Bounds are more honest than false precision. If a motor draws 0.2–0.5 A at 5 V, its electrical power is 1–2.5 W. A 10 Wh source would have an ideal runtime of 4–10 h; conversion loss and startup current shorten that. Keep assumptions beside the result. A common failure is mixing mA and A, producing a thousandfold error that still looks numerically tidy. Another is reporting six decimal places from rough inputs. For early build decisions, a defensible range with units beats a precise-looking fiction.

Problem

Estimate whether a USB power bank labeled 10,000 mAh at a 3.7 V nominal cell voltage can run a 5 V fan drawing 0.40 A for an eight-hour workday; assume 75% of nominal cell energy reaches the fan.

Steps

1. Convert capacity: 10,000 mAh = 10 Ah.
2. Nominal cell energy is 3.7 V × 10 Ah = 37 Wh; do not multiply cell-rated ampere-hours by the 5 V USB output.
3. Apply the delivery factor: 37 Wh × 0.75 = 27.75 Wh usable.
4. Fan power is 5 V × 0.40 A = 2.0 W; runtime is 27.75 Wh / 2.0 W = 13.9 h.

Result

The estimate exceeds eight hours with roughly 5.9 h of modeled margin.

Sanity check

Eight hours needs 2.0 W × 8 h = 16 Wh, less than 27.75 Wh. The estimate ignores battery shutoff behavior and fan startup current, which should be tested.

A sensor is specified to draw 600 µA. Which current in amperes should be used in a power equation?

A. 0.0006 A B. 0.006 A C. 0.6 A D. 600,000 A

Your answer: ______________________________

Reasoning:

Goal

Estimate and then measure the runtime-relevant current of a low-voltage USB fan.

Equipment

• 5 V USB fan
• USB inline voltage/current meter
• USB power bank
• timer
• notes sheet

Procedure

1. Read the fan and power-bank labels without opening either device; record units and label uncertainty.
2. Predict fan power and eight-hour energy from the rated values before connecting it.
3. Connect the inline meter, run the fan for two minutes, and record the displayed voltage and current every 30 seconds.
4. Deliberately restrict the fan inlet with a card held outside the guard, without touching the blades; diagnose whether current rises, falls, or stays similar.
5. Remove the card and confirm that readings return toward the initial range.

What to observe

• Expected: measured voltage remains near 5 V and current is of the same order as the label; actual readings must be recorded rather than replaced by the expectation.
• Expected fault clue: inlet restriction changes airflow and may change current slightly; the sign depends on fan design, so the actual direction is evidence, not a pass/fail target.

Transfer challenge

Estimate the daily energy of a small USB screen or camera using its label, then state a plausible low/high range and the assumption that dominates it.

Cautions

• Use only intact low-voltage USB equipment; do not open a mains-powered fan, charger, or power bank.
• Keep cards, hair, and fingers outside the blade guard.

Learner: ____________________ Date: ____________________

Evidence artifact or file: ____________________________________________

Notes: