Download Resistors, Currents and All That Jazz

Chapter 19 – Young & Geller
RESISTORS, CURRENTS AND ALL THAT
JAZZ
Date
Day
Topic
14-Sep
16-Sep
Monday
Wednesday
Complete Capacitors
7AM Problem Session
Chapter 19 - DC Circuits
18-Sep
Friday
Chapter 19 - DC Circuits
21-Sep
Monday
Chapter 19 - DC Circuits
23-Sep
Wednesday
EXAMINATION #1
September 23
Date
Day
Topic
14-Sep
16-Sep
Monday
Wednesday
Complete Capacitors
7AM Problem Session
Chapter 19 - DC Circuits
18-Sep
Friday
Chapter 19 - DC Circuits
21-Sep
Monday
Chapter 19 - DC Circuits
23-Sep
Wednesday
EXAMINATION #1
CHAPTER 19
Read the chapter – Important stuff
 HW assigned

Current
L
A
+
V
NOTE
 Electric Current is DEFINED as the flow of
POSITIVE CHARGE.
 It is really the electrons that move, so the current is
actually in the opposite direction to the actual flow of
charge. (Thank Franklin!)
Charge is moving so there must be an E in the metal
conductor!
Electrons
“Bounce Around”
ANOTHER DEFINITION
current I
J

area
A
A closed circuit
Ohm
 A particular object will
resist the flow of current.
 It is found that for any
conducting object, the
current is proportional to
the applied voltage.
 STATEMENT: DV=IR
 R is called the resistance
of the object.
 An object that allows a
current flow of one
ampere when one volt is
applied to it has a
resistance of one OHM.
Ohm’s Law
DV  IR
RESISTIVITY AND RESISTANCE
  0 1   (T  T0 )
Not Everything Follows Ohm’s Law
Neither does this ……
The Battery
+
-
A REAL Power Source
is NOT an ideal battery
Internal Resistance
V
E or Emf is an idealized device that does an
amount of work E to move a unit charge
from one side to another.
By the way …. this is called a circuit!
A Physical (Real) Battery
Emf
i
rR
Back to Potential
Change in potential as one circuits
this complete circuit is ZERO!
Represents a charge in space
Consider a “circuit”.
This trip around the circuit is the same as a
path through space.
THE CHANGE IN POTENTIAL FROM “a”
AROUND THE CIRCUIT AND BACK TO “a” is
ZERO!!
To remember
 In a real circuit, we can neglect the resistance of the wires
compared to the resistors.

We can therefore consider a wire in a circuit to be an
equipotential – the change in potential over its length is
slight compared to that in a resistor
 A resistor allows current to flow from a high potential to
a lower potential.
 The energy needed to do this is supplied by the battery.
DW  qDV
  ing things up
SERIESSeries
Resistors
Combinations
V1  iR1
i
V2  iR2
i
and
R1
R2
V1
V2
V
V  V1  V2  iR  iR1  iR2
R  R1  R2
general :
R ( series )   Ri
i
The rod in the figure is made of two materials. The
figure is not drawn to scale. Each conductor has a
square cross section 3.00 mm on a side. The first
material has a resistivity of 4.00 × 10–3 Ω · m and is
25.0 cm long, while the second material has a
resistivity of 6.00 × 10–3 Ω · m and is 40.0 cm long.
What is the resistance between the ends of the rod?
Parallel Combination??
R1, I1
R2, I2
V
V  iR
V V V
i  i1  i2  

R1 R2 R
so..
1
1
1


R1 R2 R
general
1
1

R
i Ri
What’s This???
In this Figure, find the
equivalent resistance
between points
(a) F and H and [2.5]
(b) F and G. [3.13]
 (a) Find the equivalent resistance between
points a and b in the Figure.
 (b) A potential difference of 34.0 V is applied
between points a and b. Calculate the current in
each resistor.
Back to Potential
Change in potential as one circuits
this complete circuit is ZERO!
Represents a charge in space
Consider a “circuit”.
This trip around the circuit is the same as a
path through space.
THE CHANGE IN POTENTIAL FROM “a”
AROUND THE CIRCUIT AND BACK TO “a” is
ZERO!!
To remember
 In a real circuit, we can neglect the resistance of the wires
compared to the resistors.

We can therefore consider a wire in a circuit to be an
equipotential – the change in potential over its length is
slight compared to that in a resistor
 A resistor allows current to flow from a high potential to
a lower potential.
 The energy needed to do this is supplied by the battery.
DW  qDV
Some Circuits are HARDER than OTHERS!
NEW LAWS PASSED BY THIS SESSION OF THE
FLORIDUH LEGISLATURE.
 LOOP EQUATION
 The sum of the voltage drops (or rises) as one completely
travels through a circuit loop is zero.
 Sometimes known as Kirchoff’s loop equation.
 NODE EQUATION
 The sum of the currents entering (or leaving) a node in a
circuit is ZERO
Take a trip around this circuit.
Consider voltage DROPS:
-E +ir +iR = 0
or
E=ir + iR
START by assuming a
DIRECTION for each Current
Let’s write the equations.
In the figure, all the resistors have a resistance of 4.0 W and
all the (ideal)
batteries have an emf of 4.0 V. What is the current through
resistor R?
RC Circuit
 Initially, no current
through the circuit
 Close switch at (a) and
current begins to flow until
the capacitor is fully
charged.
 If capacitor is charged and
switch is switched to (b)
discharge will follow.
Close the Switch
I need to use E for E
Note RC = (Volts/Amp)(Coul/Volt)
= Coul/(Coul/sec) = (1/sec)
Time Constant
  RC
Result q=CE(1-e-t/RC)
q=CE(1-e-t/RC) and i=(CE/RC) e-t/RC
E t / RC
i e
R
Discharging a Capacitor
qinitial=CE BIG SURPRISE! (Q=CV)
i
iR+q/C=0
dq q
R
 0
dt C
solution
q  q0 e t / RC
q0 t / RC
dq
i

e
dt
RC
Power
In time Dt, a charge DQ is pushed through
the resistor by the battery. The amount of work
done by the battery is :
DW  VDQ
Power :
DW
DQ
V
 VI
Dt
Dt
Power  P  IV  I IR   I 2 R
E2
P  I R  IV 
R
2