1. Lecture 24: FRI 13 MAR DC circuits III Ch27.4-9 Physics 2113
Jonathan Dowling
Lecture 24: FRI 13 MAR
DC circuits III
Ch27.4-9

2. One Battery? Simplify! Resistors Capacitors Key formula: V=iR Q=CV
In series: same current dQ/dt same charge Q
Req=∑Rj /Ceq= ∑1/Cj
In parallel: same voltage same voltage
1/Req= ∑1/Rj Ceq=∑Cj
P = iV = i2R = V2/R
U = QV/2 = Q2/2C = CV2

3. Many Batteries? Loop & Junction!
Three Batteries: Straight to Loop & Junction
One Battery: Simplify First

4. RC Circuits: Charging a Capacitor
In these circuits, current will change for a while, and then stay constant.
We want to solve for current as a function of time i(t)=dq/dt.
The charge on the capacitor will also be a function of time: q(t).
The voltage across the resistor and the capacitor also change with time.
To charge the capacitor, close the switch on a.
VC=Q/C
VR=iR
A differential equation for q(t)! The solution is:
Time constant: τ = RC
Time i drops to 1/e. CE
i(t)
E/R

5. RC Circuits: Discharging a Capacitor
Assume the switch has been closed on a for a long time: the capacitor will be charged with Q=CE.
+++
---
Then, close the switch on b: charges find their way across the circuit, establishing a current. C + -
Solution:
i(t)
E/R

8. Too Many Batteries!

10. Fire Hazard: Filling gas can in pickup truck with plastic bed liner.
Safe Practice: Always place gas can on ground before refueling.
Touch can with gas dispenser nozzle before removing can lid.
Keep gas dispenser nozzle in contact with can inlet when filling.