Circuit Problem (1)
ÎThe
light bulbs in the circuit are identical. What happens
when the switch is closed?
‹ (a)
both bulbs go out
‹ (b) the intensity of both bulbs increases
‹ (c) the intensity of both bulbs decreases
‹ (d) A gets brighter and B gets dimmer
‹ (e) nothing changes
Before: Potential at (a) is 24V, but so
is potential at (b) because equal
resistance divides 48V in half. When the
switch is closed, nothing will change
since (a) and (b) are still at same potential.
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Circuit Problem (2)
ÎBulbs
A and B are identical. What happens when the
switch is closed?
‹ (a)
‹ (b)
‹ (c)
‹ (d)
‹ (e)
nothing happens
A gets brighter, B dimmer
A gets dimmer, B brighter
Both A and B get brighter
Both A and B get dimmer
Before: Bulb A and bulb B both have
9V across them.
After: Bulb A has 12V across it and
bulb B has 6V across it (these
potentials are forced by the batteries).
PHY2054: Chapter 18
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Calculate Currents
i2 = i1 + i3
1
+12 − 3i2 = 0
2
+6 − 3i1 = 0
i2 = 4
i1 = 2
i3 = 4 − 2 = 2
PHY2054: Chapter 18
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Res-Monster Maze
2
All batteries are 4V
All resistors are 4Ω
Find current in R. (Hint: Find voltages
along path not connected by resistors)
PHY2054: Chapter 18
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Res-Monster Maze (Part 2)
All batteries are 4V
All resistors are 4Ω
Find currents across
these resistors
PHY2054: Chapter 18
37
Light Bulbs
ÎA
three-way light bulb contains two filaments that can be
connected to the 120 V either individually or in parallel.
‹A
three-way light bulb can produce 50 W, 100 W or 150 W, at the
usual household voltage of 120 V.
‹ What are the resistances of the filaments that can give the three
wattages quoted above?
Use P = V2/R
¾R1 = 1202/50 = 288Ω (50W)
¾R2 = 1202/100 = 144Ω (100W)
PHY2054: Chapter 18
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Problem
ÎWhat
is the maximum number of 100 W light bulbs you
can connect in parallel in a 100 V circuit without tripping a
20 A circuit breaker?
‹ (a)
‹ (b)
‹ (c)
‹ (d)
‹ (e)
1
5
10
20
100
Each bulb draws a current of 1A. Thus
only 20 bulbs are allowed before the
circuit breaker is tripped.
PHY2054: Chapter 18
39
RC Circuits
ÎCharging
a capacitor takes time in a real circuit
‹ Resistance
allows only a certain amount of current to flow
‹ Current takes time to charge a capacitor
ÎAssume
uncharged capacitor initially
‹ Close
switch at t = 0
‹ Initial current is i = V
ÎCurrent
/ R (no charge on capacitor)
flows, charging capacitor
‹ Generates
capacitor potential of q/C
ΔVresistor = V − q / C = Ri
ÎCurrent
‹ Goes
i
V
decreases continuously as capacitor charges!
to 0 when fully charged
PHY2054: Chapter 18
40
Analysis of RC Circuits
ÎCurrent
ÎSo
and charge are related
i = dq / dt
can recast previous equation as “differential equation“
dq
q
V
+
=
dt RC R
V − q / C = Ri
ÎGeneral
−t / RC
solution is q = CV + Ke
‹ (Check
and see!)
‹ K = −CV (necessary to make q = 0 at t = 0)
ÎSolve
for charge q and current i
(
q = CV 1 − e −t / RC
)
i=
dq V −t / RC
= e
dt R
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Charge and Current vs Time
(For Initially Uncharged Capacitor)
(
q ( t ) = q0 1 − e
i ( t ) = i0e
PHY2054: Chapter 18
−t / RC
)
−t / RC
42
Exponential Behavior
Ît
= RC is the “characteristic time” of any RC circuit
‹ Only
Ît
t / RC is meaningful
= RC
‹ Current
falls to 37% of maximum value
‹ Charge rises to 63% of maximum value
Ît
=2RC
‹ Current
falls to 13.5% of maximum value
‹ Charge rises to 86.5% of maximum value
Ît
=3RC
‹ Current
falls to 5% of maximum value
‹ Charge rises to 95% of maximum value
Ît
=5RC
‹ Current
falls to 0.7% of maximum value
‹ Charge rises to 99.3% of maximum value
PHY2054: Chapter 18
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Discharging a Capacitor
ÎConnect
fully charged capacitor to a resistor at t = 0
q
−iR − = 0
S
C
C
R
dq
q
+
=0
dt RC
ÎGeneral
‹K
−t / RC
solution is q = Ke
= CV (necessary to make have full charge at t = 0)
ÎSolve
for charge q and current i
q = CVe
−t / RC
dq
V −t / RC
=− e
= − I 0e−t / RC
i=
dt
R
PHY2054: Chapter 18
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Charge and Current vs Time
(For Initially Charged Capacitor)
q ( t ) = q0e
−t / RC
i ( t ) = i0e
−t / RC
PHY2054: Chapter 18
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