RC Circuits Lecture Notes

Introduction

• Topic: RC Circuits, combining resistors and capacitors in circuits.
• Focus: Dynamics of charging and discharging capacitors over time.
• Presenter: Chad from Chad's Prep.
• Resources: Comprehensive playlists and premium master courses on Chadprep.com; prep courses for DAT, MCAT, and OAT.

Importance and Application

• Example: Defibrillator as a practical application of RC circuits.
  • Paddles act as plates of a capacitor, requiring time to charge before discharging to the patient's chest.

RC Circuit Basics

• Diagram Explanation: Typically involves multiple switches to control the loop of the circuit.
• Charging Process:
  • Close the loop with the battery, resistor, and capacitor in series.
  • Current flows, charging the capacitor, leading to transient current.
  • Current max at the start, decreases until the capacitor is fully charged.
  • Fully charged: Current stops completely.
• Discharging Process:
  • Open circuit for battery and close loop with resistor and capacitor.
  • Charged capacitor discharges through the resistor.
  • Initial max current decreases until fully discharged.

Graphs and Mathematical Analysis

• Charging:

  • Charge buildup (Q) on capacitor plates: Exponential approach to max value.
  • Equation: Q = C * ΔV_max * (1 - e^(-t/RC))
  • Time constant (τ = RC): Greater RC = longer charging time.
  • Approximately 5τ to reach over 99% charge.
  • Voltage across capacitor (ΔV) behaves similarly to charge (Q).
  • Current (I) starts max, exponentially decreases to zero.

• Discharging:

  • Similar but reverse exponential process.
  • Charge (Q) and voltage (ΔV) start max, decrease to zero.
  • Equation: Q = Q_max * e^(-t/RC) and similar for ΔV.
  • Current (I) also decreases from max to zero.
  • Approximately 5τ to reach over 99% discharge.*

Example Calculation

• Given: 12V battery, 100Ω resistor, 6mF capacitor.
• Find:
  1. Time Constant: τ = R * C = 0.6 seconds
  2. Fully Charged: Q_max = C * ΔV = 72μC
  3. After 1.8 seconds:
     • Charge (Q): Q_t = Q_max * (1 - e^(-t/τ)) = 68μC
     • Voltage (ΔV): ΔV = Q / C = 11V*

Conclusion

• Recap: Explained the dynamics of RC circuits, graphs, equations, and performed example calculations.
• Recommendation: Like the video if found helpful, and happy studying!