Ph272- General Physics II (Electricity and
Magnetsism)
Lecture 12: Ch. 26 - RC Circuits
Key Topics
Overview
- We will study the physical process of discharging and charging
a capactor.
- We will set up and solve the differential equations which
describe the discharging and charging processes.
- The SAME differential equations also describe radioactive
decay process, population growth, etc... it is worthwhile to
study them in details.
Discharging a capacitor
- We will talk about discharging a capacitor first because
the differential equation is easier.
- Circuit setup: In every circuit there is always some
amount of resistance so we have a charged capacitor (with charge
Q) in series with a resistor.
- What are the initial conditions?
What is the initial charge stored in the capacitor?
What is the initial voltage across the capacitor?
What is the initial voltage across the resistor?
What is the initial current through the circuit?
- Physical Process: As time goes by, what happens?
How do the charge, the voltage across the capacitor, voltage
across the resistor, and the current behave with time? Sketch
these quantities vs. time. Can you guess the mathematical functions
for these curves?
- Set up differential equation for Q(t) : (Do this in
class) - This is a "first-order, linear, homogenous"
differential equation (DE). In physics, homogenous DE means no
driving term
- Solve the differential equation and match the initial
condition. In physics, we call the homogenous solution the
"transcient" solution.
- New Term: Time constant of a RC circuit
-> Do Problem 23-9, 23-11, P. 774.
Charging a capacitor
- Circuit setup: We have an uncharged capacitor
in series with a battery source and a resistor.
- What are the initial conditions?
What is the initial charge stored in the capacitor?
What is the initial voltage across the capacitor?
What is the initial voltage across the resistor?
What is the initial current through the circuit?
- Physical Process: As time goes by, what happens?
How do the charge, the voltage across the capacitor, voltage
across the resistor, and the current behave with time? Sketch
these quantities vs. time. Can you guess the mathematical functions
for these curves?
- Set up differential equation for Q(t) : (Do this in
class) - This is a "first-order, linear, inhomogenous"
differential equation. In physics, inhomogenous DE means there
is a driving term (the battery)
- Solve the differential equation and match the initial
condition. The solution of an inhomogenous DE consists of
a steady state part and a transcient part.
->Do Problem 23-12, P. 774.
-> What if the capacitor was partially charged at t=0?
Repeat your sketches for this case.
Application
- Example: Camera flash light circuit (simplified).
Review
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