understand that the resistance of a light-dependent resistor (LDR) decreases as the light intensity increases

Resistance and Resistivity

Resistance (\$R\$) quantifies how strongly a material opposes the flow of electric current. It depends on the material’s intrinsic property – resistivity (\$\rho\$) – and on its geometry (length \$L\$ and cross‑sectional area \$A\$).

Key definitions

• Resistance (\$R\$): \$R = \dfrac{V}{I}\$, where \$V\$ is the potential difference and \$I\$ is the current.
• Resistivity (\$\rho\$): a material constant, measured in \$\Omega\!\cdot\!{\rm m}\$. It relates to resistance by \$R = \rho \dfrac{L}{A}\$.
• Conductivity (\$\sigma\$): the reciprocal of resistivity, \$\sigma = 1/\rho\$.

Ohm’s law and resistance

For an ohmic conductor, the current is directly proportional to the applied voltage:

\$ V = IR \$

If the material is non‑ohmic, the \$V\$–\$I\$ relationship is not linear, and the resistance may vary with \$V\$, \$I\$, temperature, or other external factors.

Resistivity

The resistivity of a material can change with temperature (\$T\$). For many metals a good approximation is:

\$ \rho(T) = \rho0 \bigl[1 + \alpha (T - T0)\bigr] \$

where \$\rho0\$ is the resistivity at a reference temperature \$T0\$ and \$\alpha\$ is the temperature coefficient of resistivity.

Light‑Dependent Resistor (LDR)

An LDR, also known as a photoresistor, is a semiconductor device whose resistance changes markedly with the intensity of incident light. It is widely used in light‑sensing circuits such as automatic street lights, camera exposure controls, and alarm systems.

Construction and operation

The active element of an LDR is a thin film of a high‑resistivity semiconductor (typically cadmium sulfide, CdS) deposited on an insulating substrate. Photons with sufficient energy excite electrons from the valence band to the conduction band, increasing the number of charge carriers and thereby reducing the material’s resistivity.

Dependence of resistance on light intensity

Empirically, the resistance of an LDR follows a power‑law relationship with the illuminance \$I\$ (measured in lux):

\$ R = k \, I^{-\alpha} \$

where:

• \$k\$ is a constant that depends on the specific device and its geometry,
• \$\alpha\$ is the light‑sensitivity exponent (typically \$0.5 \le \alpha \le 1\$).

Thus, as the light intensity \$I\$ increases, the exponent \$-\alpha\$ makes \$R\$ decrease.

Typical resistance values

Experimental verification

1. Set up a simple circuit: connect the LDR in series with a known resistor \$R_{\text{ref}}\$ and a DC power supply (e.g., 5 V).
2. Measure the voltage across the LDR (\$V_{\text{LDR}}\$) using a voltmeter for several light conditions (dark, dim, bright).
3. Calculate the LDR resistance using Ohm’s law:

   \$ R{\text{LDR}} = \frac{V{\text{LDR}}}{I} = \frac{V{\text{LDR}}}{(V{\text{supply}}-V{\text{LDR}})/R{\text{ref}}} \$

4. Record the corresponding illuminance with a lux meter.
5. Plot \$\log(R_{\text{LDR}})\$ against \$\log(I)\$. The slope of the straight line gives \$-\alpha\$, confirming the power‑law relationship.

Summary

• Resistance \$R\$ depends on resistivity \$\rho\$, length \$L\$, and area \$A\$ of a conductor.

• Resistivity is an intrinsic material property that can vary with temperature.

• An LDR is a non‑ohmic device whose resistance falls as the incident light intensity rises, following \$R = k I^{-\alpha}\$.

• Typical LDRs change from mega‑ohms in darkness to a few hundred ohms in bright sunlight.

• Experimental measurements using a simple series circuit and a lux meter can verify the inverse relationship between resistance and light intensity.