One resistor obeys Ohm's law cleanly. Two resistors combine. Three resistors combine in more ways. By the end of the week you can predict the voltage at every node of any resistor network you will see in HW-101 and beyond.
Reading (~45 min)
- Horowitz and Hill, The Art of Electronics, Ch 1 §1.2 (voltage dividers and Kirchhoff's laws). Read carefully
- Optional: the SparkFun "Voltage Dividers" tutorial online; same content, more pictures
Lecture (~2 hr)
- Series resistors. Currents are the same; voltages add. The 9V battery driving two resistors in series sees the sum of their resistances
- Parallel resistors. Voltages are the same; currents add. The combined resistance is smaller than either individual resistor (a counterintuitive result on first encounter)
- The voltage divider. Two resistors in series; tap the middle. The output voltage is a fraction of the input voltage, determined by the ratio of the two resistors. This is the most-used analog circuit in electronics; you will use it weekly for the rest of your career
- Kirchhoff's laws in plain English. The voltage law: voltages around a loop sum to zero (no energy appears from nowhere). The current law: currents into a junction equal currents out (no charge accumulates at a point). Both are conservation laws
Lab exercises (~2 hr)
Lab 2.1: Voltage Divider. Build a divider that drops 5V to 3.3V using two resistors. Measure the actual output; compare to predicted. ~90 minutes.
Independent practice (~3 hr)
- Build three different voltage dividers with different ratios (drop 5V to 2.5V; to 1.25V; to 4.5V). Measure each; tabulate predicted vs measured. Note the small errors and speculate on causes
- Build a series circuit of three different resistors. Measure the voltage drop across each one; verify Kirchhoff's voltage law
- Build a parallel circuit of two different resistors. Measure the current through each; verify Kirchhoff's current law
Reflection prompts
- The voltage-divider output depends on the ratio of resistor values, not on either value alone. When would you use 10 kΩ + 10 kΩ vs 100 Ω + 100 Ω, given both give the same ratio?
- Parallel resistors combine to a smaller resistance. Build the intuition: if a single 10 kΩ resistor lets a certain current through, what does adding a second 10 kΩ in parallel do, and why?
- Kirchhoff's laws are conservation laws. What other physical laws are conservation laws? Why do conservation laws keep appearing across different fields?
What's next
Week 3 introduces the breadboard. Every circuit from week 3 onward is built on one. The breadboard's internal wiring decides which pins are connected to which; misreading the layout is the most common source of "why doesn't my circuit work" frustration.