Sammy guidesA technician must decide whether burst terminal voltage is safe before changing pack internal resistance on the real device. The result is unresolved until the rule and units are checked. Predict the direction first.
See the relationship before changing it
The figure reads from left to right. The blue card is pack internal resistance. The middle card applies this page's rule. The green card is burst terminal voltage. 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 pack internal resistance, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 3 ohm.
- 2
Name the relationship. terminal = 1.90 V - 0.160 A x resistance
- 3
Substitute with units. 1.90 - 0.160 x 3.00 = 1.42 V
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change pack internal resistance
Try Predict the direction of terminal = 1.90 V - 0.160 A x resistance. Test another pack internal resistance, then compare burst terminal voltage.
Observe Higher pack resistance lowers the voltage available during the same radio pulse. Reset pack internal resistance to 3 and compare burst terminal voltage.
Explain Higher pack resistance lowers the voltage available during the same radio pulse.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
1. Start with the physical story
Milliamp-hours count charge. Multiplying by pack voltage estimates energy, but a radio pulse also pushes current through internal resistance. That resistance can pull terminal voltage below the regulator's input limit before the charge ledger reaches zero.
2. Name every algebra move
Convert chargeDivide 3000 mAh by 1000 and multiply by 3.0 V to get watt-hours.
Price the pulseMultiply 0.160 A by pack resistance to find voltage sag.
Find the railSubtract sag from the loaded open-circuit voltage.
Retain chargeCompound the 2.5% yearly loss over 136/365 years.
Separate sensingMultiply 2 kohm by 100 pF, then take five time constants.
3. Reproduce the chapter case
ΔV=0.160×3.00=0.480 V
Vterminal=1.90−0.480=1.42 V
retained=0.975^(136/365)=99.06%
τ=2000×100 pF=200 ns; 5τ=1.00 µs
The sensing element can settle quickly while the complete wake, bus, association, retry, and display path still takes far longer than one microsecond.
4. Try one real input
TryMove pack resistance from fresh toward aged and predict terminal voltage before reading it.
ObserveAt 3.00 ohms the same pulse loses 0.480 V and leaves 1.42 V, even though the charge-retention result stays above 99%.
ExplainSelf-discharge removes charge slowly; internal resistance removes voltage only while current flows. The two mechanisms answer different failure questions.
This is a screening ledger, not a field battery model.
- Cell curve
- Open-circuit voltage and resistance vary with chemistry, load, temperature, and state of charge.
- Active window
- Association, TLS, MQTT, retries, display, and regulator loss need measured traces.
- Sensor τ
- The component RC does not bound firmware or full-sensor readiness.
Correct, not complete: surviving this voltage calculation does not prove 136 days of environment-monitor service.
5. Use the result in the design
Measure a complete worst-case transmit trace on fresh and aged cells, then compare minimum regulator input with the lowest observed loaded voltage.
6. Record the evidence state
Keep chemistry, cell count, state of charge, temperature, open-circuit voltage, internal resistance, current trace, cutoff, retries, sensor-ready signal, and firmware version together.
7. Check yourself
Why is 3000 mAh not already an energy value?
Why can a pack brown out with charge remaining?
Does a 1 microsecond sensor 5τ prove a 200 ms active window?
The arithmetic reproduces the chapter's illustrative pack and sensor constants.
- Cell curve
- Open-circuit voltage and resistance vary with chemistry, load, temperature, and state of charge.
- Active window
- Association, TLS, MQTT, retries, display, and regulator loss need measured traces.
- Sensor τ
- The component RC does not bound firmware or full-sensor readiness.
Correct, not complete: surviving this voltage calculation does not prove 136 days of environment-monitor service.