EngiMetric Arena / Interpret & Validate
How much usable energy is in a 100 Ah battery at 80 % DoD?
Competency Evidence interpretation primary Quantitative reasoning supporting
What you should take away: Distinguish nameplate energy from usable energy at a stated depth of discharge, and avoid treating amp-hour capacity as delivered energy.
The situation
What is happening
A 12 V, 100 Ah battery is limited to 80 % depth of discharge. A colleague claims it can deliver 1.2 kWh to the load. Choose the defensible interpretation.
Given
| Quantity | Value | Unit | Note |
|---|---|---|---|
| Nominal voltage | 12 | V | Battery nominal voltage. |
| Rated capacity | 100 | Ah | Nameplate amp-hour capacity. |
| Depth of discharge | 80 | % | Maximum fraction withdrawn. |
Assumptions this challenge makes
- The nominal voltage is used for the energy conversion.
- The depth-of-discharge limit is a usable-energy limit, not an efficiency.
- Temperature, ageing and Peukert effects are not modelled.
Your call
Your answer
Hints
- Convert the nameplate to energy first: voltage x amp-hours. Keep the units.
- The depth of discharge is the fraction you are allowed to use. Apply it to the nameplate energy.
- Check the arithmetic of 80 % of 1.2 kWh before accepting either the 1.2 or the 0.8 claim.
Your answer Engine result
Where that comes from
Each limit, checked
Why
- Nameplate energy is 12 V x 100 Ah = 1.2 kWh.
- At 80 % depth of discharge, the usable energy is 1.2 x 0.8 = 0.96 kWh.
- The battery-bank engine confirms the relationship: to supply 960 Wh per day for one day at 80 % DoD, it sizes a 1,200 Wh bank, which is the same 1.2 kWh nameplate.
- The colleague’s 1.2 kWh claim is therefore the nameplate value, not the usable value. Designing a load around it would overdraw the battery beyond the stated DoD.
- The difference matters for autonomy: usable energy, not nameplate energy, is what the load can actually consume.
What this challenge does not establish
- The nominal voltage is used; real battery voltage varies with state of charge and load.
- Temperature, ageing, Peukert losses and inverter efficiency are not modelled.
- The 80 % DoD is a stated limit; a different battery technology may have a different limit.
- The calculation does not size the battery bank for a required autonomy period; it interprets one battery.