1. Physics 2112 Unit 9: Electric Current
Today’s Concept:
Electric Current

2. A Big Idea Review Coulomb’s Law Force law between point charges q1 q2
Electric Field
Force per unit charge
Property of Space
Created by Charges
Superposition
Gauss’ Law
Flux through closed surface is always proportional to charge enclosed
Gauss’ Law
Can be used to determine E field
Spheres
Cylinders
Infinite Planes
Electric Potential
Potential energy per unit charge
Electric Potential
Scalar Function that can be used to determine E
Capacitance
Relates charge and potential for two conductor system 2

3. Applications of Big Ideas
Conductors
Charges free to move
What Determines How They Move?
They move until
E = 0 !
E = 0 in conductor determines charge densities on surfaces
Spheres
Cylinders
Infinite Planes
Gauss’
Law
Field Lines & Equipotentials
Field
Lines
Equipotentials
Capacitor Networks
Series:
(1/C23) = (1/C2) + (1/C3)
Parallel
C123 = C1 + C23
Work Done By E Field
Change in Potential Energy 3

4. Key Concepts: Today’s Plan: How resistance depends on A, L, s, r
How to combine resistors in series and parallel
Understanding resistors in circuits
Today’s Plan:
Review of resistance & preflights
Work out a circuit problem in detail

5. Conductivity – high for good conductors.A L
Ohm’s Law: J = s E
Conductivity – high for good conductors. V
V = EL
I = JA
Observables:
I/A = sV/L
I = V/(L/sA)
R = L sA
I = V/R
R = Resistance
R = 1/s

6. Civil Engineering Analogy
I is like flow rate of water
V is like pressure
R is how hard it is for water to flow in a pipe
To make R big, make L long or A small
R = L sA
To make R small, make L short or A big
Battery is like a pump

7. 1 CheckPoint: Two Resistors 2
Same current through both resistors
Compare voltages across resistors

8. CheckPoint: Current Density
The SAME amount of current I passes through three different resistors. R2 has twice the cross-sectional area and the same length as R1, and R3 is three times as long as R1 but has the same cross-sectional area as R1. In which case is the CURRENT DENSITY through the resistor the smallest?

9. Circuit E is conservative force  go completely around circuit Vf = Vob c R1
E is conservative force
 go completely around circuit
Vf = Vo VB R2 d a
-IR1 V
+VB
-IR2 a b c d a

10. Resistor Summary Series Parallel Wiring Voltage Current Resistance R1
Each resistor on the same wire.
Each resistor on a different wire.
Wiring
Different for each resistor.
Vtotal = V1 + V2
Same for each resistor.
Vtotal = V1 = V2
Voltage
Same for each resistor
Itotal = I1 = I2
Different for each resistor
Itotal = I1 + I2
Current
Increases
Req = R1 + R2
Decreases
1/Req = 1/R1 + 1/R2
Resistance

11. CheckPoint: Resistor Network 1
Three resistors are connected to a battery with emf V as shown. The resistances of the resistors are all the same, i.e. R1= R2 = R3 = R.
Compare the current through R2 with the current through R3:
I2 > I3
I2 = I3
I2 < I3

12. CheckPoint: Resistor Network 2
Three resistors are connected to a battery with emf V as shown. The resistances of the resistors are all the same, i.e. R1= R2 = R3 = R.
Compare the current through R1 with the current through R2:
I1/I2=1/2
I1/I2=1/3
I1 = I2
I1/I2=2
I1/I2=3

13. CheckPoint: Resistor Network 3
Three resistors are connected to a battery with emf V as shown. The resistances of the resistors are all the same, i.e. R1= R2 = R3 = R.
Compare the voltage across R2 with the voltage across R3:
V2 > V3
V2 = V3 = V
V2 = V3 < V
V2 < V3

14. CheckPoint 2 CheckPoint 3 CheckPoint 4 R1 = R2 = R3 = R V1 V2 I1 I2
Compare the current through R1 with the current through R2
I I2
CheckPoint 3
Compare the voltage across R2 with the voltage across R3
V V3
CheckPoint 4
Compare the voltage across R1 with the voltage across R2
V V2

15. CheckPoint: Resistor Network 4
Three resistors are connected to a battery with emf V as shown. The resistances of the resistors are all the same, i.e. R1= R2 = R3 = R.
Compare the voltage across R1 with the voltage across R2.
V1 = V2 = V
V1 = 1/2 V2 = V
V1 = 2V2 = V
V1 =1/2 V2 =1/5 V
V1 =1/2 V2 = 1/2 V

16. Example 9.1 In the circuit shown: V = 18V,
R1 = 1W, R2 = 2W, R3 = 3W, and R4 = 4W.
What is V2, the voltage across R2?
Conceptual Analysis:
Ohm’s Law: when current I flows through resistance R, the potential drop V is given by: V = IR.
Resistances are combined in series and parallel combinations
Rseries = Ra + Rb
(1/Rparallel) = (1/Ra) + (1/Rb)
Strategic Analysis:
Combine resistances to form equivalent resistances
Evaluate voltages or currents from Ohm’s Law
Expand circuit back using knowledge of voltages and currents
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

17. Example 9.1 R1 R2 R1 R2 V V R3 R3 R24 R4 R1 V V R1234 R234
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

18. = Quick Follow-Ups What is I3 ? A) I3 = 2 A B) I3 = 3 A C) I3 = 4 A
I1 = I2 + I3
Make Sense? I1 I2 I3 R1 R2 V R1
R234 a b
V = 18V
R1 = 1W
R2 = 2W
R3 = 3W
R4 = 4W
R24 = 6W
R234 = 2W
V234= 12V
V2 = 4V
I1234 = 6 Amps V = R3 R4
What is I3 ?
A) I3 = 2 A B) I3 = 3 A C) I3 = 4 A
V3 = V234 = 12V
I3 = V3/R3 = 12V/3W = 4A
What is I1 ?
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
We know I1 = I1234 = 6 A

19. Electro-Motive Force (EMF),
Power In Resistors
Not a force!!
Electro-Motive Force (EMF),
Energy provided to make charges move, units of V
=VI (for a battery)
= I2R (for resistor)

20. Example 9.2 In the circuit shown: V = 18V,
R1 = 1W, R2 = 2W, R3 = 3W, and R4 = 4W.
How much electrical energy does the battery put into the circuit every second in the previous problem?
How much electrical energy does each resistor turn into thermal energy every second?
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

21. Parallel and Series (with color)V R1 R2 R4 R3
If every electron that goes through one element must go through another, those two are in series.
If two sides of two elements can be connected by different colored lines, those two are in parallel. .
If two points are connected by a line not containing any circuit elements those point are at the same potential.