The Big Idea
Last Time:
- Analysis of multi-loop circuits with batteries and resistors.
- Main Feature: Currents are attained instantaneously and do not vary with time!!
Today:
- Just added a capacitor to the circuit.
- What changes??
- KVL yields a differential equation with a term proportional to q and a term proportional to I = dq/dt.
http://wug.physics.uiuc.edu/courses/phys112/fall97/acts/lect11/act11a/sld001.htm
- Physically, what’s happening is that the final charge cannot be placed on a capacitor instantly.
- Initially, the voltage drop across an uncharged capacitor = 0 because the charge on it is zero ! (V=Q/C)
- As current starts to flow, charge builds up on the capacitor, the voltage drop is proportional to this charge and increases; it then becomes more difficult to add more charge so the current slows