Week 4: Capacitors and RC Circuits

Capacitors store energy. When you charge a capacitor through a resistor, the capacitor fills up over time, not instantly. The time it takes is the "time constant." By the end of the week you can build an RC circuit that takes a measurable second or two to charge, and you can explain what the time constant means in plain English.

Reading (~45 min)

• Horowitz and Hill, The Art of Electronics, Ch 1 §1.4 (capacitors and RC circuits). Read carefully
• The kit's capacitor identification card; the markings on ceramic and electrolytic capacitors are different

Lecture (~1.5 hr)

• What a capacitor is. Two conductive plates separated by an insulator. When you apply a voltage across the plates, charge accumulates on each plate
• Charging through a resistor. The resistor limits the rate of charge flow; the capacitor fills up exponentially over time
• The time constant τ = R × C. After one time constant, the capacitor is at ~63% of its final voltage. After three time constants, it is at ~95%. After five, you can call it "fully charged" for practical purposes
• Ceramic vs electrolytic. Ceramic capacitors are small and unpolarized; electrolytics are larger, have a polarity, and store more charge. Mistake: putting an electrolytic in backward. It can pop. Use the kit's smaller-valued electrolytics for the early labs

Figure 4.1. The shape every capacitor traces every time it charges or discharges through a resistor. The amber three dots are the practical thresholds: at one τ the cap is "obviously charging," at three τ it is "close enough for most things," at five τ it is "done for any purpose that does not require precision." Predict the curve in Lab 4.1 before you scope it; the surprise when the scope trace matches the math is the lesson.

Lab exercises (~2 hr)

Lab 4.1: RC Timing. Build a 100 kΩ + 100 μF circuit; measure the time it takes for the capacitor to charge from 0 V to ~3 V. Compare to the predicted τ. ~90 minutes.

Independent practice (~3 hr)

• Build three different RC circuits with different time constants. Measure each. Tabulate predicted vs measured. The accuracy of your measurements tells you something about the tolerance of your parts
• Try the same circuit with a ceramic capacitor instead of electrolytic. Notice how the time constant changes (ceramic is much smaller capacitance per package)
• Read the kit's electrolytic capacitor datasheet. Find the tolerance specification (typically ±20% for electrolytics). Notice that your "predicted" time constant is only good to ±20% even before measurement error enters

Reflection prompts

1. The capacitor charges fastest when it is most empty. As it fills up, the charge rate slows. Why? Use the water-pipe analogy or your own
2. Time constant τ = R × C. If you wanted a 10-second time constant, what specific R and C values would you pick? Why those values rather than other valid combinations?
3. The capacitor "remembers" how much charge it has stored. In what sense is this memory? How long does the memory last?

What's next

Week 5 returns to LEDs, with more depth. You will pick the right current-limiting resistor for any LED at any voltage, and you will understand why the wrong resistor either gives no light or a brief flash followed by a wisp of smoke.