1. Ideal vs Real Battery Ideal battery: no internal energy dissipation
Energy conservation
Work done by battery is equal to energy dissipated in resistor
EMF  = terminal voltage V
Real battery: internal energy dissipation exists
dW > i2Rdt or  > iR=V

2. Real Battery = Resistors in Series
The current through devices in series is always the same.
Req i ε
terminal voltage
internal resistance
For multiple resistors in series:

3. Resistors in Parallel Generally, •••
Devices in parallel has the same potential drop
Generally,
•••

4. Kirchhoff’s Rules Kirchhoff’s Rule 1: Loop Rule
When any closed loop is traversed completely in a circuit, the algebraic sum of the changes in potential is equal to zero.
Coulomb force is conservative
Kirchhoff’s Rule 2: Junction Rule
The sum of currents entering any junction in a circuit is equal to the sum of currents leaving that junction.
Conservation of charge
In and Out branches
Assign Ii to each branch

5. Kirchhoff’s Loop Rule Example
When any closed loop is traversed completely in a circuit, the algebraic sum of the changes in potential is equal to zero.
where is the potential difference across i-th device in the circuit:
positive if potential rises
negative if potential drops
terminal voltage

6. Loop Example with Two EMF Devices
IR1
IR2 ε2
Ir2
IR3 ε1
Ir1
If 1 <2, we have I<0 !? Þ
This just means the actual current flows reverse to the assumed direction. No problem!

7. Finding Potential and Power in a Circuit
But what is I? Must solve for I first!
supplied by 12V battery
Just means 0 V here
dissipated by resistors
The rest?
into 4V battery (charging)

8. Charging a Battery Positive terminal to positive terminal
Charging EMF > EMF of charged device
battery being charged (11V)
good battery (12V)
Say, R+r1+r2=0.05 (R is for jumper cables). Then,
power into battery 2
If connected backward,
Large amount of gas produced
Huge power dissipation in wires

9. Using Kirchhoff’s Laws in Multiple Loop Circuits
Identify nodes and use Junction Rule:
Identify independent loops and use Loop Rule:
Only two are independent.

10. Circuit Analysis Tips Sketch the diagram
Simplify using equivalent resistors
Label currents with directions
Use Junction Rule in labeling
Choose independent loops
Use Loop Rule
Solve simultaneous linear equations

11. Another example (with parallel R combos)
I1+I2 I2
Sketch the diagram
Simplify using equivalent resistors
Label currents with directions
Use Junction Rule in labeling
Choose independent loops
Use Loop Rule
Solve simultaneous linear equations I1
Replace by equivalent R=2 first.

12. Ammeter and Voltmeter Ammeter: an instrument used to measure currents
It must be connected in series.
The internal resistance of an ammeter must be kept as small as possible.
Voltmeter: an instrument used to measure potential differences
It must be connected in parallel.
The internal resistance of a voltmeter must be made as large as possible.

13. Galvanometer Inside Ammeter and Voltmeter
Galvanometer: a device that detects small currents and indicates its magnitude. Its own resistance Rg is small for not disturbing what is being measured.
shunt resistor
galvanometer
Ammeter: an instrument used to measure currents
Voltmeter: an instrument used to measure potential differences
galvanometer