Physics
ys cs 132:
3 Lecture
ectu e 15
5
Elements of Physics II
A
Agenda
d for
f T
Today
d


Resistance
 Resistors
 Series
 Parallel
 Ohm’s law
Electric Circuits
 Current
 Kirchhoff
Kirchhoff’s
s laws
Physics 201: Lecture 1, Pg 1
Electromotive force




Electromotive force (emf) is the maximum
potential difference a battery or power source
can give a circuit.
A car b
battery h
has an emff off 12 V
Sometimes shown as a script (E)
Symbol for emf
-
+
Physics 201: Lecture 1, Pg 2
Electrical Current
When we connect the two terminals of an emf to
a circuit ( a continuous conducting path), charge
will move continuously through the circuit.


Since there is a potential difference electrons in circuit will feel
a force

emf
Electrons will flow in
direction of positive
terminal
 Battery “pushes”
electrons
Physics 201: Lecture 1, Pg 3
Electrical Current

This flow is called electric current

Net amount of charge through a point in the
circuit per unit time.

Units Ampere = Coulomb/second
q
I
t
Physics 201: Lecture 1, Pg 4
Example
The electron drift speed in a wire is exceedingly
slow-typically only a fraction of a millimeter per
second. Yet when you turn on a flashlight switch,
the light comes on almost instantly. Resolve this
apparent paradox.
Physics 201: Lecture 1, Pg 5
Clicker Question 1:
When a light
g bulb is emitting
g light
g in a circuit as
below the number of electrons entering the light
bulb is:
(a) larger than the number leaving the light bulb
(b) equal to the number leaving the light bulb
(c) smaller than the number leaving the light bulb
Physics 201: Lecture 1, Pg 6
Plinko




Disks = electrons
Disk bounces through
atoms on it’s way down the
incline
Angle
g of incline = emf
(potential difference)
Y t b demo
Youtube
d
Physics 201: Lecture 1, Pg 7
Resistance

Resistance: Traveling through a conductor, electrons bump into
things which slows them down
down.
 : Resistivity: Density of bumps
 L: Length of conductor
 A: Cross sectional area of conductor
R ρ

L
A
A
All electrical devices will resist the flow
of electrical current
L
Physics 201: Lecture 1, Pg 8
R ρ
L
A
Plinko
Physics 201: Lecture 1, Pg 9
Clicker Question 2:
Below we have a skinny wire and a thick wire
connected to identical batteries. Which case
will have the larger current?
Iskinny

( ) Thick Wire
(a)
(b) Skinny Wire
(c) They will have the same current
Ithick

Physics 201: Lecture 1, Pg 10
Clicker Question 3:
Below we have circuit with a resistor and a wire. Which part will have
the larger current?
?
(a) Wire
(b) Resistor
(c) They will have the same current
Iwire

Iresistor
Physics 201: Lecture 1, Pg 11
Conservation of Current
Physics 201: Lecture 1, Pg 12
Charge Distribution

The nonuniform distribution of surface charges along a
wire creates a net electric field inside the wire that points
from the more p
positive end toward the more negative
g
end
of the wire.

This is the internal electric field that pushes the electron
current through the wire
wire.
Physics 201: Lecture 1, Pg 13
Clicker Question 4:
Is this a possible surface charge distribution for a current carrying
wire?
?
(a) yes
(b) no
Physics 201: Lecture 1, Pg 14
Electric Current

The direction of current flow – from the positive terminal to
the negative one – was decided before it was realized that
electrons are negatively charged
charged. Therefore
Therefore, current flows
around a circuit in the direction a positive charge would
move; electrons move the other way. However, this does
not matter in most circuits.
circuits
Physics 201: Lecture 1, Pg 15
Kirchhoff’s Junction Law
For a junction, the law of
conservation of current
requires that
where the  symbol
y
means summation.
This basic conservation
statement is called
Kirchhoff’s junction
law
law.
Physics 201: Lecture 1, Pg 16
Kirchhoff s Loop Law
Kirchhoff’s
Voltage drops must add to zero

We can think of the voltage difference as a height
difference
I
Down
Volts

R
Up
Volts
Electron must end up at same place it started!!
Physics 201: Lecture 1, Pg 17
Ohm’s law

With conductors the more resistance the less
current can flow

•
Ohm’s law
V  IR
Hi h resistance
Higher
i t
llower currentt

Units are Ohms ()
V
I 
R
Physics 201: Lecture 1, Pg 18
Resistor

A device that resists current

Used to
o co
control
o cu
current
e flow
o in a ccircuit
cu

Resistor in a circuit:

Generally in a circuit the resistance of the
connecting wires are very small and we can
neglect them.

Wires will resist current, but we will assume they have zero
resistance!!
Physics 201: Lecture 1, Pg 19
Kirchhoff s Loop Law
Kirchhoff’s
for the Simplest Circuit in the World
I

R
• Example
– Calculate I when emf =24 Volts and R = 8 
– Ohm’s Law: V=IR
– I = 24/8 = 3 Amps
Physics 201: Lecture 1, Pg 20
Clicker Question 5:
Below we have two circuits, with identical batteries and three identical
cylindrical conductors. Compare
C
the current in the two circuits:
(a) IA > IB
(b) IA = IB
(c) IA < IB


Circuit A
Circuit B
Physics 201: Lecture 1, Pg 21
Clicker Question 6:

A light bulb is connected to a battery in case A.
In case B an identical light bulb is added in
series. What happens to the brightness of the
original bulb?
(a) it stays the same
(b) it decreases
(c) it increases
Case A
Case B
Physics 201: Lecture 1, Pg 22
Series wiring


When two objects are connected end to end in a circuit, they are
said
id tto b
be iin series.
i
Here R1 and R2 are in series
R1
R2

Current must be same in each resistor!!
Voltage drop across R1 plus Voltage drop across R2
should equal the emf of the battery
Physics 201: Lecture 1, Pg 23
Resistors in series

One wire:
 If charge goes through one resistor, it must go
through other.
 I1 = I2 = Ieq
 V1 + V2 = Veq

Add eq
1
2
 Adding Voltage IR1 + IR2=I(R1 + R2)
 Adding length Req=(L1+L2)/A
R
=R +R
R1
Req
R2

The equivalent resistance of resistors in series is just
the addition of the resistors
Physics 201: Lecture 1, Pg 24
Clicker Question 7:
In the circuit below, what is the voltage across R1?
a) 12 V
b) zero
R1 = 4 
R2 = 2 
c) 6 V
d) 8 V
e) 4 V
12 V
Physics 201: Lecture 1, Pg 25
Clicker Question 7:
In the circuit below, what is the voltage across R1?
R1 = 4 
R2 = 2 
12 V
Physics 201: Lecture 1, Pg 26
Clicker Question 8:
Below we have two circuits, with identical batteries and three identical
cylindrical conductors. Compare
C
the current drawn ffrom the
batteries in the two circuits:
(a) IA > IB
(b) IA = IB
(c) IA < IB


Circuit A
Circuit B
Physics 201: Lecture 1, Pg 27
Parallel wiring

If two objects are in a circuit such that both ends
of the object are connected, they are said to be in
parallel.


The current splits and travels through
R1and R2 separately
R1
R2
Voltage drop across resistors must be same as emf of the battery.
Physics 201: Lecture 1, Pg 28
Resistors in parallel

Two wires:
 Both ends of resistor are connected
 I1 + I2 = Ieq
 V1 = V2 = Veq
R1

Add
R2
Req
1/Req = 1/R1 + 1/R2
 Adding Current V/R1+V/R2=V(1/R1+1/R2)
 Adding Area
Physics 201: Lecture 1, Pg 29
Clicker Question 9:
In the circuit below,, what is the current through
g R1?
a) 10 A
b) zero
c) 5 A
d) 2 A
R2 = 2 
R1 = 5 
e) 7 A
10 V
Physics 201: Lecture 1, Pg 30
Clicker Question 9:
In the circuit below, what is the current through R1?
R2 = 2 
R1 = 5 
10 V
Physics 201: Lecture 1, Pg 31