RC Circuit Charging and Discharging

📋 Course Outline

1. RC Circuit Components and Charging
2. Differential Equation of Charge
3. Current and Capacitor Voltage
4. Graphical Study of Charging
5. Series Resistors and Time Constant
6. Experimental Determination of Parameters
7. Energy and Charging Speed

📖 1. RC Circuit Components and Charging

📝 Essential Points

• The RC circuit contains an ideal voltage generator of electromotive force E, an ohmic conductor of resistance R, a previously discharged capacitor of capacitance C, and a switch K.

• When switch K is closed at t = 0, the capacitor undergoes charging until the switch is opened at t = 40 ms.

💡 Memory Hook

Close K → current flows → capacitor charges → permanent regime

📖 2. Differential Equation of Charge

🔑 Key Concepts & Definitions

• Time constant : $\tau=RC$ and characterizes the speed of capacitor charging.

📝 Essential Points

📐 Formula — For a series RC circuit, the charge satisfies $RC\frac{dq(t)}{dt}+q(t)=CE$, so the differential-equation constants are $\alpha=RC$ and $\beta=CE$.