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NOTES
Ideal vs Real Battery
•  Ideal battery: no internal
energy dissipation
Energy conservation
Work done by battery is equal
to energy dissipated in resistor
EMF ε = terminal voltage V
•  Real battery: internal
energy dissipation exists
dW > i2Rdt or ε > iR=V
Resistors in Series
  The current through devices
in series is always the same.
i
R1
R2
ε
For multiple
resistors in series:
i
i
Req
ε
Real Battery = Resistors in Series
  The current through devices in series is always the same.
i
Req
terminal
voltage
ε
internal
resistance
For multiple
resistors in series:
Resistors in Parallel
Devices in parallel has the
same potential drop
Generally,
•••
DOCCAM 1 DEMO 5B-04
SUM OF VOLTAGE DROPS EQUALS EMF
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
Loop Example with Two EMF Devices
Ir1
IR1
IR2
ε2
ε1
Ir2
IR3
If ε1 <ε2, we have I<0 !?
This just means the actual
current flows reverse to the
assumed direction. No problem!
Finding Potential and Power in a Circuit
But what is I? Must
solve for I first!
supplied by
12V battery
The rest?
Just means
0 V here
into 4V battery
(charging)
dissipated by
resistors
Charging a Battery
•  Positive terminal to positive terminal
•  Charging EMF > EMF of charged device
good
battery
(12V)
Say, R+r1+r2=0.05Ω (R is for jumper cables).
Then,
battery being
charged (11V)
power into battery 2
•  If connected backward, NO !!
  Large amount of gas produced
  Huge power dissipation in wires
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.
Same example (with parallel R combos)
I1+I2
I2
•  Sketch the diagram
•  Simplify using equivalent resistors
I1
•  Label currents with directions
•  Use Junction Rule in labeling
•  Choose independent loops
•  Use Loop Rule
Replace by equivalent
R=2Ω first.
•  Solve simultaneous linear equations
NOTES
Loop currents directly (with parallel R combos)
I1
I2
I1 -I2
•  Sketch the diagram
•  Simplify using equivalent resistors
•  Label loop currents with directions
•  Use Loop currents I1 and I2
•  Choose interior clockwise loops
. Set up cononical equations in
Replace by equivalent
R=2Ω first.
. I1
I2
Ε format
I1 (12 +6) +I2 (-6) = +18 (Emf)
Left loop
I1 (-6) + I2 (6+3+2) =+21 (Emf)
Right loop
Note Symmetry of 2 Equations in 2 unknowns
Kirchoff Circuit Analysis Tips
(Loop current system easier)
•  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
(Loop current system easier !!)
DOCCAM 1 DEMO 5B03
MULTIMETERS AND VOLTAGE PARADOX
Basic 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.
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.
galvanometer
Ammeter: an instrument
used to measure currents
shunt resistor
Voltmeter: an instrument
used to measure potential
differences
galvanometer
NOTES
PHYS 241 – Extra Quiz 3
What is the magnitude of the current through R2 ?
a.  0.33A
b.  2.5A
c.  0.75A
d.  1.5A
e. 0.5A
10Ω
10Ω
15V
R1
R3 10Ω
R2
15V
PHYS 241 – Extra Quiz 3
What is the current through R3 ?
a.  0.375A
b.  0.5A
c.  0.75A
d.  1A
e.  1.5A
20Ω
20Ω
30V
R1
R3 20Ω
R2
30V