Math Bridge: LED Voltage Budget

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Math BridgeElectronicsStruggle-friendly runway

Where did the missing LED current go?

Use Kirchhoff voltage accounting to size an LED resistor and expose the missing-current pitfall.

Eddie, the electronics guideEddie guides
The one targetAccount for the LED drop before sizing its series resistor.
The chapter case5 V rail, 2.0 V red LED, and a 20 mA target.
What it buys youA current-setting resistor based on the voltage it actually sees.

A field team faces an unresolved physical question: Where did the missing LED current go? They must answer it before changing led drop on the real device. Predict the direction first.

See the relationship before changing it

The figure reads from left to right. The blue card is led drop. The middle card applies this page's relationship. The green card is resistor 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 added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.

LED drop changes resistor voltage An input card leads through the page relationship to the resistor voltage result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. Kirchhoff accounting couples the component drop to current; ignoring one series drop cannot be repaired by later rounding.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for led drop is 2.

  2. 2

    Name the relationship. VR=5.0-2.0=3.0 V Rcorrect=3.0/0.020=150 ohm Rwrong=5.0/0.020=250 ohm Iactual=3.0/250=12.0 mA shortfall=40.0%

  3. 3

    Substitute the chapter fixture. Set led drop to 2. The page ledger gives resistor voltage as 3.00 V.

  4. 4

    Read the result. Keep V beside the value. Use it only inside the technical boundary on this page.

Predict, then change led drop

Try Predict the direction of resistor voltage. Move one control, calculate, then check your prediction.

2
Chapter baseline
Resistor voltage

Observe Kirchhoff accounting couples the component drop to current; ignoring one series drop cannot be repaired by later rounding. Reset the control to 2 and compare resistor voltage.

Explain Only led drop moves here. The other chapter fixtures remain fixed.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only led drop moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only led drop. It replays the chapter fixture; it is not a field prediction.

1. Start with the physical story

Every volt around a series loop must be spent once. The LED claims its forward drop first; the resistor receives only the remainder.

Eddie: A large resistor can be mathematically tidy and still be wrong if it was given the whole supply.

2. Name every algebra move

1

Write the loopVsupply=IR+Vf.

2

Isolate the resistor voltageVR=Vsupply−Vf.

3

Size the resistorR=VR/Itarget.

4

Replay the mistakeRwrong=Vsupply/Itarget.

5

Find real currentIactual=VR/Rwrong.

3. Reproduce the chapter case

VR=5.0−2.0=3.0 V
Rcorrect=3.0/0.020=150 Ω
Rwrong=5.0/0.020=250 Ω
Iactual=3.0/250=12.0 mA
shortfall=40.0%

The wrong design is dim rather than dramatic, which is why this bookkeeping error survives reviews.

4. Try one real input

TryMove the control, predict the direction, then compare every output.

LED drop
Resistor voltage
Correct resistor
Wrong resistor
Actual current
Current shortfall
Resistor power
12-bit ADC step

ObserveA larger LED drop leaves less voltage for the resistor, so the correct resistance and actual current both fall while the shortcut stays frozen at 250 Ω.

ExplainKirchhoff accounting couples the component drop to current; ignoring one series drop cannot be repaired by later rounding.

Technical boundaries.

This is a transparent first-order teaching ledger tied to the chapter constants.

LED model
Forward voltage is treated as fixed at the chosen operating point.
Tolerance
Real Vf, resistor value, supply voltage, and temperature all vary.
Drive
GPIO current and package power limits still need separate checks.

Correct, not complete: this ledger does not qualify an LED, resistor, GPIO, or thermal design.

5. Use the result in the design

Choose a worst-case Vf range, calculate current at both ends, select a standard resistor, then verify pin current and resistor power.

6. Record the evidence state

Record supply tolerance, LED Vf bin and test current, resistor tolerance, measured loop current, temperature, and GPIO limits.

7. Check yourself

Why subtract Vf?
Answer: The resistor only receives the supply voltage left after the series LED drop.
Why can the bad design look harmless?
Answer: It produces a lower current and a dim LED rather than an immediate overcurrent failure.
Is a fixed Vf exact?
Answer: No. It is a local approximation; use datasheet curves and worst-case bins for release work.
Honesty boundary.

The arithmetic reproduces the named chapter case; it is an inspectable model, not a component approval.

LED model
Forward voltage is treated as fixed at the chosen operating point.
Tolerance
Real Vf, resistor value, supply voltage, and temperature all vary.
Drive
GPIO current and package power limits still need separate checks.

Correct, not complete: this ledger does not qualify an LED, resistor, GPIO, or thermal design.

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