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NOTES
Resistors in Parallel and Series
i
R1
R2
ε
i
The same example (with parallel R combos)
I3
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.
I3 = I 1 + I 2
•  Solve simultaneous linear equations
Loop current example (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 Equations
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
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.
DEMO 6B-08 CLASSICAL GALVANOMETER
ELECTRONIC VOLT- AMPERE - OHM, METER
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
CAPACITOR IN RC CIRCUITS - TRANSIENTS
I
I
charging
discharging
ε
  Switch closed at t=0. C initially
uncharged, thus V0 = 0 across C
and I0 = ε/R initially.
  Switch closed at t=0. C
initially charged, thus V0 = Q0/C
across C and I0 = V0/R initially.
  After a long time, C is fully
charged and VC = ε across C
and I∞ = 0.
  After a long time, C is fully
discharged and VC = 0 across C
and I∞ = 0.
time constant
Q = Q f (1 − e
−t / RC
)
Discharging a Capacitor in RC Circuits Eqns
1.  Switch closed at t=0. Initially C
is fully charged with Q0
2.  Loop Rule:
3.  Convert to a differential equation
I
4.  Solve it!
Q(t) during Discharging
time constant
0.37Q0
Current I(t) during Discharging
DEMO 6C-03
FLASHER CIRCUIT
6C03
Charging a Capacitor in RC Circuits
1.  Switch closed at t=0
C initially uncharged, thus zero
voltage across C.
2.  Loop Rule:
3.
Convert to a differential equation
4.  Solve it!
(τ=RC is the time constant again)
Charge Q(t) during Charging
time constant
Current I(t) during Charging
Broken circuit = RC R in Lamp
110V
C very small. i.e. RC very
small. Instantly discharged
BEHAVIOR OF CAPACITORS
•  Charging
–  Initially, the capacitor behaves like a wire.
–  After a long time, the capacitor behaves like an OPEN switch.
•  Discharging
–  Initially, the capacitor behaves like a battery.
–  After a long time, the capacitor behaves like an OPEN switch
DOCCAM 2
ONE FARAD CAPACITOR and LED RESISTOR
ENERGY CONSERVATION IN DISCHARGING A CAPACITOR
Discharging:
Energy
lost by C
Power dissipated by R
Energy Conservation in Charging a Capacitor
Charging:
Work done
by battery
Energy
stored in C
The rest?
Power dissipated by R
  Independent of R
What if R=∞ ?
What if R=0 ?
PHYS 241 – Extra Quiz 3
All the capacitors below are identical and so are all
the resistors. Which circuit have the longest time
constant?
A
C
B
D
E
PHYS 241 – Extra Quiz 3
All the capacitors below are identical and so are all
the resistors. Which circuit have the shortest time
constant?
A
C
B
D
E