Published by Patrick Mutisya · 14 days ago
A potential divider (or voltage divider) is a simple resistive network that produces a fraction of an input voltage. For two series resistors \$R1\$ and \$R2\$ connected across a supply \$V{\text{in}}\$, the output voltage taken across \$R2\$ is
\$\$
V{\text{out}} = V{\text{in}} \frac{R2}{R1 + R_2}
\$\$
This relationship is the basis for many sensor circuits, where the resistance of one element varies with a physical quantity such as temperature or light intensity.
A thermistor is a resistor whose resistance varies strongly with temperature. Two main types are used:
The resistance–temperature relationship is often approximated by the linear form
\$\$
RT = R0\,[1 + \alpha (T - T_0)]
\$\$
where \$R0\$ is the resistance at a reference temperature \$T0\$ and \$\alpha\$ is the temperature coefficient (typically \$10^{-3}\,\text{K}^{-1}\$ for NTC devices).
When a thermistor \$RT\$ is placed as \$R2\$ in a divider, the output voltage becomes a direct indicator of temperature:
\$\$
V{\text{out}}(T) = V{\text{in}} \frac{RT}{R{\text{fixed}} + R_T}
\$\$
| Thermistor Type | Typical \$R_0\$ (Ω) at 25 °C | Typical \$\alpha\$ (K⁻¹) | Application Example |
|---|---|---|---|
| NTC | 10 kΩ | +3.9 × 10⁻³ | Room‑temperature monitoring |
| PTC | 1 kΩ | −2.5 × 10⁻³ | Over‑current protection |
Design Example
Suppose \$V{\text{in}} = 5\,\$V, a 10 kΩ NTC thermistor (\$\alpha = 3.9\times10^{-3}\,\text{K}^{-1}\$) and a fixed resistor \$R{\text{fixed}} = 10\,\$kΩ. The output voltage at 20 °C and 30 °C is:
\$\$
\begin{aligned}
R_{20} &= 10\,\text{k}\Omega[1 + 3.9\times10^{-3}(20-25)] = 9.805\,\text{k}\Omega,\\
V_{\text{out}}(20) &= 5 \frac{9.805}{10 + 9.805}=2.48\ \text{V},\\[4pt]
R_{30} &= 10\,\text{k}\Omega[1 + 3.9\times10^{-3}(30-25)] = 10.195\,\text{k}\Omega,\\
V_{\text{out}}(30) &= 5 \frac{10.195}{10 + 10.195}=2.55\ \text{V}.
\end{aligned}
\$\$
The change of about 70 m \cdot over a 10 °C interval can be amplified or read directly by an ADC.
An LDR (or photoresistor) changes its resistance according to the intensity of incident light. The relationship is non‑linear and is often expressed as
\$\$
R_L = K\,E^{-\gamma}
\$\$
where \$E\$ is the illuminance (lux), \$K\$ and \$\gamma\$ are material‑dependent constants (typical \$\gamma\$ ≈ 0.5–0.7).
Placing the LDR as \$R_2\$ gives
\$\$
V{\text{out}}(E) = V{\text{in}} \frac{K\,E^{-\gamma}}{R_{\text{fixed}} + K\,E^{-\gamma}}
\$\$
Thus the output voltage rises as light intensity falls (for an LDR used as the lower resistor).
| Parameter | Typical \cdot alue (Dark) | Typical \cdot alue (Bright) |
|---|---|---|
| Resistance \$R_L\$ (Ω) | 1 MΩ (≈ 0 lux) | 1 kΩ (≈ 10 000 lux) |
| Response Time | \overline{30} ms | \overline{10} ms |
Design Example
With \$V{\text{in}} = 12\,\$V, \$R{\text{fixed}} = 5\,\$kΩ, and an LDR whose resistance varies from \$100\,\$kΩ (dark) to \$2\,\$kΩ (bright):
\$\$
\begin{aligned}
V_{\text{out}}(\text{dark}) &= 12 \frac{100}{5 + 100}=11.4\ \text{V},\\[4pt]
V_{\text{out}}(\text{bright}) &= 12 \frac{2}{5 + 2}=3.43\ \text{V}.
\end{aligned}
\$\$
The large voltage swing makes the LDR‑divider suitable for light‑level detection in robotics or automatic lighting control.
| Sensor | Typical Resistance Range | Output \cdot oltage Trend | Common Applications |
|---|---|---|---|
| NTC Thermistor | 1 kΩ – 100 kΩ (20 °C – 100 °C) | Decreases with temperature (if placed as \$R_2\$) | Temperature monitoring, thermostats |
| PTC Thermistor | 100 Ω – 10 kΩ (20 °C – 100 °C) | Increases with temperature (if placed as \$R_2\$) | Over‑current protection, self‑regulating heaters |
| LDR (Photoresistor) | 1 kΩ – 1 MΩ (bright – dark) | Decreases with light intensity (if placed as \$R_2\$) | Ambient light sensing, automatic lighting, robotics |