1. Current = charges in motion
Electric Current
Current = charges in motion
Magnitude
rate at which net positive charges move across a cross sectional surface
Units: [I] = C/s = A (ampere)
J = current density (vector) in A/m²
Current is a scalar, signed quantity, whose sign corresponds to the direction of motion of net positive charges by convention

2. Ohm’s Law constant R Ohm’s Law Power dissipation : RV R I
Resistance (definition)
constant R Ohm’s Law
Power dissipation :

3. EMF – Electromotive Force
An EMF device is a charge pump that can maintain a potential difference across two terminals by doing work on the charges when necessary.
Examples: battery, fuel cell, electric generator, solar cell, fuel cell, thermopile, …
Converts energy (chemical, mechanical, solar, thermal, …) into electrical energy.
Within the EMF device, positive charges are lifted from lower to higher potential.
If work dW is required to lift charge dq,
EMF

4. Resistors in Series
The current through devices in series is always the same.
Req i ε R1 R2 i ε
For multiple resistors in series:
Same equation for parallel connected capacitors

5. Real Battery = Resistors in Series
The current through devices in series is always the same.
Req i ε
terminal voltage
internal resistance
Show the demo of old battery before and after closing the switch.

6. Resistors in Parallel Same equation for capacitors connected in serial
Devices in parallel has the same potential drop
Generally,
Same equation for capacitors connected in serial

7. 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

8. Circuit Analysis Tips Simplify using equivalent resistors
Label currents with arbitary directions
If the calculated current is negative, the real direction is opposite to the one defined by you.
Apply Junction Rule to all the labeled currents.
Useful when having multiple loops in a circuit.
Choose independent loops and define loop direction
Imaging your following the loop and it’s direction to walk around the circuit.
Use Loop Rule for each single loop
If current I direction across a resistor R is the same as the loop direction, potential drop across R is ∆V = −I×R, otherwise, ∆V = I×R
For a device, e.g. battery or capacitor, rely on the direction of the electric field in the device and the loop direction to determine the Potential drop across the device
Solve simultaneous linear equations
Current dirction is the moving direction of positive charge, i.e. the electric field direction, therefore, following the current direction, potential drops

9. Loop Example with Two EMF DevicesÞ
If 1 <2, we have I<0 !?
This just means the actual current flows reverse to the assumed direction. No problem!

10. 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
Current dirction is the moving direction of positive charge, i.e. the electric field direction, therefore, following the current direction, potential drops
dissipated by resistors
The rest?
into 4V battery (charging)

11. 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

12. 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.

13. Warm-up quiz (a). 2.0A (b). 1.0A (c). -2.0A (d). -1.0A
I1+I2 I2
What’s the current I1 ? I1
(a). 2.0A
(b). 1.0A
(c). -2.0A
(d). -1.0A
(e). Need more information to calculate the value.

14. Answer for the Warm-up quiz
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.

15. 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.

16. 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

17. What is the current through R1 ?
PHYS241 – Quiz 11A
What is the current through R1 ?
30
30
0.575A
0.5A
0.75A
0.33A
1.5A R1 R2
45V
45V R3
30

18. What is the current through R2 ?
PHYS241 – Quiz11B
What is the current through R2 ?
10
10
0.33A
2.5A
0.75A
1.5A
0.5A R1 R2
15V
15V R3
10

19. What is the current through R3 ?
PHYS241 – Quiz 11C
What is the current through R3 ?
20
20
0.375A
0.5A
0.75A 1A
1.5A R1 R2
30V
30V R3
20