Phoebe guidesA field team faces an unresolved physical question: Why equal light ratios make shrinking voltage steps They must answer it before changing ldr gamma exponent on the real device. Predict the direction first.
See the relationship before changing it
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.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline for ldr gamma exponent is 0.7.
- 2
Name the relationship. R(E)=R_ref(E/E_ref)^(-γ); V_out=V_s R_fixed/(R_LDR+R_fixed)
- 3
Substitute the chapter fixture. Set ldr gamma exponent to 0.7. The page ledger gives r at 1,000 lux as 0.398 kohm.
- 4
Read the result. Keep kohm beside the value. Use it only inside the technical boundary on this page.
Predict, then change ldr gamma exponent
Try Predict the direction of r at 1,000 lux. Move one control, calculate, then check your prediction.
Observe The resistance readouts use the chapter's power law. The voltage readouts put those same resistances into its 3.3 V divider equation. Reset the control to 0.7 and compare r at 1,000 lux.
Explain Only ldr gamma exponent moves here. The other chapter fixtures remain fixed.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
1. Read a power law in words
E is light level. R is LDR resistance. The minus sign means resistance falls as light rises. γ controls how steeply it falls.
2. Bound the exponent with recombination
At steady state, carrier generation G balances recombination R(n): dn/dt=G−R(n)=0. If recombination is proportional to n, then n∝E and γ=1. If it is proportional to n², then n∝√E and γ=0.5. The chapter's γ=0.7 sits between those ideal limits.
3. Work the resistance points
At 10 luxR=10 kΩ.
At 100 luxR=10×10^(−0.7)=1.995 kΩ, about 2.0 kΩ.
At 1,000 luxR=10×100^(−0.7)=0.398 kΩ, about 0.4 kΩ.
4. Try the exponent γ
TryMove γ between the 0.5 and 1.0 physical limits and watch the same three light points.
ObserveAt γ=0.7, equal 10× light jumps give 1.101 V and then only 0.423 V.
ExplainThe resistance readouts use the chapter's power law. The voltage readouts put those same resistances into its 3.3 V divider equation.
The divider calculation fixes its supply, reference resistance, and fixed resistor, using one light-response exponent over the comparison range. It does not establish that exponent outside its fitted light and temperature range or model differences between devices, illumination history, slow response, and sensor, converter, or motor-driver saturation.
- Real LDRs vary by unit, remember prior illumination, respond slowly, and may saturate with the ADC or motor driver
- Needs separate evidence
Use field evidence or a deeper model before release.
5. Turn resistance into divider voltage
At 10 lux this is 1.650 V. At 100 lux it is 2.751 V. At 1,000 lux it is 3.174 V. The voltage rises because the top LDR resistance falls.
6. Connect the curve to behaviour
The first light decade moves the motor command much more than the second. Near bright light, a left-right lux difference can make only a small voltage difference. The vehicle becomes less sensitive even though the physical light still changes.
7. Check yourself
What does the minus sign in E^(−γ) mean?
Why does 100 lux give about 2.0 kΩ?
Why are the two voltage steps unequal?
The divider calculation fixes its supply, reference resistance, and fixed resistor, using one light-response exponent over the comparison range. It does not establish that exponent outside its fitted light and temperature range or model differences between devices, illumination history, slow response, and sensor, converter, or motor-driver saturation.
- 10 kΩ at 10 lux
- Reference light-dependent resistance and illuminance
- γ=0.7
- Light-response power-law exponent
- 10 kΩ fixed resistor
- Divider resistance connected to ground
- 3.3 V supply
- Divider supply voltage
- 2.0/0.4 kΩ
- Rounded resistances at brighter reference light levels
- 1.65/2.75/3.17 V
- Rounded divider voltages across three light levels
- 1.995
- Resistance at one hundred lux in kilohms
- 0.398
- Resistance at one thousand lux in kilohms
- 2.751
- Divider voltage at one hundred lux in volts
- 3.174
- Divider voltage at one thousand lux in volts
- 1.101
- First tenfold-light voltage increment in volts
- 0.423 results keep extra digits only to show the calculation
- Second tenfold-light voltage increment in volts
The simple power law is not a production calibration.