Lab 12 Black Box - Part 2

12.1 Light Bulb

About the light bulb: similar to the diode, the light bulb has a non-linear \(I-V\) curve. Even though the light bulb contains a metallic filament, which is ohmic, the temperature increases dramatically during operation, so that its resistance is affected. Our light bulb can be roughly modelled with a square root shape:

\(I = \alpha V^{0.5}\)

where \(\alpha\) = 60 mA. The arguments are the same as for the diode. However, given that the slope for small electric potentials is high and then becomes small, means that the resistance is large initially and becomes smaller at high voltages.

12.2 Goals

  1. Practice the process of drawing a schematic diagram of a circuit, predict the shape of the I-V curve, and compare with the measurements.
  2. Figure out the circuit inside a black box by analysis of its \(I-V\) characteristics.
  3. Solve a box from level 1 and then move to a level 2 box, or even a level 3 box.

12.3 Equipment

  1. Black box
  2. Variable voltage source (0.1 V – 3.0 V)
  3. 2x DMM and wires

12.4 Procedure

  1. Get a black box
  2. Connect the power supply to the two outputs of the black box.
  3. Use two DMMs to measure the current and the electric potential
  4. Measure an I-V curve. Then reverse the polarity on the power supply and measure the negative side of the I-V curve, so that you vary the voltage from -3 V to +3 V. Make sure you have a sufficient number of data points near the interesting areas.
  5. Analyze the I-V curve data and determine what is inside the box. Make a schematic drawing and check with the instructor whether you have the correct circuit.
  6. When you find the correct circuit, move to the next level.

It helps to follow these guiding steps:

  • Determine the elements that could potentially go into the circuit;
  • Propose a circuit based on the elements;
  • Determine the I-V curve for the propose circuit and compare qualitatively with the measured circuit;
  • Modify your proposed circuit until it qualitatively matches the measurements;
  • Determine the resistances from the inverse slope, remember \(R = \Delta V / \Delta I\), where \(\Delta V = V_f - V_i\), and \(\Delta I = I_f - I_i\). As before, make sure to choose small differences in electric potential, maybe 0.5V or less.

12.5 Graph

Draw the I-V curve; include units and label the axes. Make sure to include the schematic diagram that shows how the resistors, diodes are arranged inside the black box.

12.6 Summary

Discuss your approach to finding the circuit inside the black box.