Phoebe guidesSee the relationship before changing it
The figure reads from left to right. The blue card is sensor daily charge. The middle card applies this page's rule. The green card is ideal life without cell leak. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only sensor daily charge, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 0.07 mAh/day.
- 2
Name the relationship. life = 1,000 mAh / sensor daily charge
- 3
Substitute with units. 1,000 / 0.070 = 14,286 days
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change sensor daily charge
Try Predict the direction of life = 1,000 mAh / sensor daily charge. Test another sensor daily charge, then compare ideal life without cell leak.
Observe Larger daily sensor charge shortens ideal life before yearly cell leak. Reset sensor daily charge to 0.07 and compare ideal life without cell leak.
Explain Larger daily sensor charge shortens ideal life before yearly cell leak.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
1. Capacity and current must share units
A battery capacity of 1,000 mAh means it could ideally supply 1,000 mA for one hour, or a smaller current for longer. The chapter gives sensor use as 0.070 mAh each day, so first turn that daily charge into an average current.
2. Reproduce the sensor-only result
Average current0.070 mAh/day ÷ 24 h/day=0.00292 mA=2.92 µA.
Lifetime hours1,000 mAh ÷ 0.00292 mA=342,857 h.
Lifetime days342,857/24=14,286 days, about 14,300.
3. Turn yearly loss into current
At 1% per year, the simple model allocates 1,000×0.01=10 mAh of lost capacity over 8,760 hours.
Divide loss by timeI_self=10 mAh/8,760 h=0.00114 mA=1.14 µA.
Add the drainsI_total=2.92+1.14=4.06 µA.
4. Try the self-discharge rate
TryMove the simple yearly self-discharge rate from 0% to 3% while capacity and sensor use stay fixed.
ObserveAt 1%, self-discharge is 1.14 µA; total current is 4.06 µA and the simple result falls to 10,267 days, or 28.1 years.
ExplainThe widget converts both drains to average current, adds them, and divides the same 1,000 mAh capacity by that total.
A constant percent-per-year current is a teaching approximation.
- Cell voltage, load pulses, temperature, usable-capacity derating, seal and electrolyte aging, MCU current, conversion losses, and shelf-life limits shorten real service
- Needs separate evidence
Use field evidence or a deeper model before release.
5. Recompute the corrected division
The self-discharge term alone removes roughly one quarter of the sensor-only 14,286-day result.
6. Stop where the model stops
The answer is still not a deployment promise. The chapter says CR-series cells are commonly rated for roughly a decade of shelf life, and it already warns that the microcontroller dominates real systems. Once the arithmetic exceeds chemical life, report the chemical limit instead of extra false precision.
7. Check yourself
How does 0.070 mAh/day become 2.92 µA?
What current represents 1% yearly loss from 1,000 mAh?
Is 28.1 years a promised field lifetime?
These are the chapter inputs, worked results, and named teaching assumptions.
- 1,000 mAh CR2477
- Charge or energy value
- 0.070 mAh/day
- Time, interval, or service-life value
- about 14,300 days
- Time, interval, or service-life value
- catalog-typical 1% yearly self-discharge
- Named teaching assumption
- 1.14 µA
- Current or responsivity value
- 4.06 µA
- Current or responsivity value
- 10,267 days
- Time, interval, or service-life value
- 28.1 years
- Time, interval, or service-life value
- shelf-life warning come from the chapter
- Chapter input or worked result
The constant-current equivalent is useful bookkeeping, not a battery-aging law or warranty.