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Announcements
From last time
•WebAssign HW Set 5 due this Friday
• Problems cover material from Chapters 18
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emf
Internal resistance
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Resistors in Series
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• My office hours today from 2 – 3 pm
• or by appointment (I am away next week)
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•Exam 1 8:20 – 10:10 pm Wednesday, February 16
• Covers Ch. 15-18
• 20 questions
• You should bring:
• 8 ½ x 11 in formula sheet (handwritten
only!)
• Calculator (no cell phones) + spare
batteries
• pencils (spares)
• UF ID
• Room assignments:
Terminal voltage ΔV = ε – Ir
Same current
Req = R1 + R2 + R3 + …
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Resistors in parallel
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Same voltage drop
1
1
1
1
=
+
+
+…
R eq R1 R 2 R 3
QUESTIONS? PLEASE ASK!
Kirchhoffʼs Rules
1. Junction Rule
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Sum of the currents entering a
junction = the sum of the currents
leaving the junction
Σ Iin = Σ Iin
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Conservation of charge
More About the Loop Rule
I1 = I 2 + I 3
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2. Loop Rule
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Sum of the ΔV across all the
elements around any closed circuit
loop must be zero
Σ Vloop = 0
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A statement of Conservation of
Energy
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Traveling around the loop
from a to b
In (a), the resistor is
traversed in the direction
of the current, the
potential across the
resistor is –IR
In (b), the resistor is
traversed in the direction
opposite of the current,
the potential across the
resistor is +IR
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Problem-Solving Strategy
– Kirchhoffʼs Rules
Even More About the Loop
Rule
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In (c), the source of
emf is traversed in the
direction of the emf
(from – to +), the
change in the electric
potential is +ε
In (d), the source of
emf is traversed in the
direction opposite of
the emf (from + to -),
the change in the
electric potential is -ε
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Example Problem 18.26
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A dead battery is
charged by
connecting it to a
live battery of
another car with
jumper cables.
Determine the
amount of current in
the starter and in
the dead battery.
Draw the circuit diagram and assign labels
and symbols to all known and unknown
quantities
Assign directions to the currents.
Apply the junction rule to any junction in
the circuit
Apply the loop rule to as many loops as
are needed to solve for the unknowns
Solve the equations simultaneously for the
unknown quantities
Check your answers
RC Circuits
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DC circuits containing
capacitors and resistors,
having time-varying
currents/charges
When S is closed, the
capacitor starts to charge
The capacitor charges until it
reaches its maximum charge
(Qmax = Cε)
Once the capacitor is fully
charged, I à 0
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Charging Capacitor in an
RC Circuit
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Notes on Time Constant
The charge on the
capacitor varies with
time
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q(t) = Qmax(1 – e-t/RC)
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Can define a time
constant:
τ = RC
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τ is the time required
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for the q to increase
from zero to 63.2% (=
1 – e) of its maximum
Discharging Capacitor in
an RC Circuit
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When a charged
capacitor is placed in
the circuit, it can be
discharged
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q = Qe-t/RC
The charge decreases
exponentially
At t = τ = RC, the
charge decreases to
0.368 Qmax
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In a circuit with a large time
constant, the capacitor charges
very slowly
The capacitor charges very quickly
if there is a small time constant
After t = 10 τ, the capacitor is over
99.99% charged
Example Problem 18.33
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Consider a series RC
circuit for which R =
1.0 MΩ, C = 5 µF,
and ε = 30 V. Find
the charge on the
capacitor 10 s after
the switch is closed.
In other words, in one
time constant, the
capacitor loses 63.2% of
its initial charge
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Solution to 18.26
Solution to 18.33
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