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Electricity & Magnetism Lecture 11 Today’s Concept: RC Circuits Electricity & Magne7sm Lecture 11, Slide 1
Electricity & MagnetismLecture 11
Today’s Concept:
RC Circuits
Electricity & Magne7sm Lecture 11, Slide 1
RC Circuit (Charging)
Kirchhoff’s Voltage Rule
Short Term (q = q0 = 0)
Long Term (Ic = 0)
RVbattery
Ca
b
Intermediate
a
RVbattery
C
b
Capacitor uncharged, Switch is moved to posi?on “a”
Electricity & Magne7sm Lecture 11, Slide 2
CheckPoints 2 & 4
Close S1, V1 = voltage across C immediately a@er
V2 = voltage across C a long 7me a@er
A) V1 = V V2 = VB) V1 = 0 V2 = VC) V1 = 0 V2 = 0
D) V1 = V V2 = 0
Electricity & Magne7sm Lecture 11, Slide 3
Kirchhoff’s Voltage Rule
Short Term (q = q0)
Long Term (Ic = 0)
RC Circuit (Discharging)
RVbattery
Ca
b
IntermediateV
Capacitor has q0 = CV, Switch is moved to posi?on “b”
RVbattery
Ca
bI+ −
−I
Electricity & Magne7sm Lecture 11, Slide 4
+
−
CheckPoint 6
ABCD
Electricity & Magne7sm Lecture 11, Slide 5
ABC
CheckPoint 8
Electricity & Magne7sm Lecture 11, Slide 6
What will happen aFer I close the switch?
A) Both bulbs come on and stay on.B) Both bulbs come on but then bulb 2 fades out.C) Both bulbs come on but then bulb 1 fades out.D) Both bulbs come on and then both fade out.
VC
S
Bulb 1
Bulb 2
R
R
DEMO – Clicker Question 1
Electricity & Magne7sm Lecture 11, Slide 8
Suppose the switch has been closed a long ?me.Now what will happen aFer open the switch?
A) Both bulbs come on and stay on.B) Both bulbs come on but then bulb 2 fades out.C) Both bulbs come on but then bulb 1 fades out.D) Both bulbs come on and then both fade out.
VC
S
Bulb 1
Bulb 2
R
R
DEMO – Clicker Question 2
Electricity & Magne7sm Lecture 11, Slide 9
In this circuit, assume V, C, and Ri are known.
C ini7ally uncharged and then switch S is closed.
What is the voltage across the capacitor a@er a long 7me ?
Conceptual Analysis: Circuit behavior described by Kirchhoff’s Rules:
KVR: Σ Vdrops = 0 KCR: Σ Iin = Σ Iout
S closed and C charges to some voltage with some 7me constant
Strategic AnalysisDetermine currents and voltages in circuit a long 7me a@er S closed
Calculation
Electricity & Magne7sm Lecture 11, Slide 10
V
R1 R2
CR3
S
Immediately a@er S is closed: what is I2, the current through C what is VC, the voltage across C?
A) Only I2 = 0 B) Only VC = 0 C) Both I2 and VC = 0 D) Neither I2 nor VC = 0
Why?We are told that C is ini7ally uncharged (V = Q/C)I2 cannot be zero because charge must flow in order to charge C
CalculationIn this circuit, assume V, C, and Ri are known.C ini7ally uncharged and then switch S is closed.
What is the voltage across the capacitor a@er a long 7me ?
Electricity & Magne7sm Lecture 11, Slide 11
V
R1 R2
C
R3
S
Immediately a@er S is closed, what is I1, the current through R1 ?
I1
CalculationIn this circuit, assume V, C, and Ri are known.C ini7ally uncharged and then switch S is closed.
What is the voltage across the capacitor a@er a long 7me ?
Electricity & Magne7sm Lecture 11, Slide 12
A B C D E
Calculation
V
R1 R2
CR3
S
A@er S has been closed “for a long 7me”, what is IC, the current through C ?
A B C
In this circuit, assume V, C, and Ri are known.C ini7ally uncharged and then switch S is closed.
What is the voltage across the capacitor a@er a long 7me ?
Electricity & Magne7sm Lecture 11, Slide 13
V
R1 R2
CR3
S In this circuit, assume V, C, and Ri are known.C ini7ally uncharged and then switch S is closed.
What is the voltage across the capacitor a@er a long 7me ?
Calculation
Electricity & Magne7sm Lecture 11, Slide 14
A@er S has been closed “for a long 7me”, what is VC, the voltage across C ?
A B C D E
Q(t) = Q0e�t/RC
0
0.2500
0.5000
0.7500
1.0000
0 2.5000 5.0000 7.5000 10.0000
“Frac?on of ini?al charge that remains”
“How many ?me constants worth of ?me that have elapsed”
How do Exponentials Work?
Electricity & Magne7sm Lecture 11, Slide 16
Q(t) = Q0e�t/RC
0
0.2500
0.5000
0.7500
1.0000
0 2.5000 5.0000 7.5000 10.0000
RC = 1
RC = 2
Time constant:τ = RC
The bigger τ is,the longer it takes to getthe same change…
Electricity & Magne7sm Lecture 11, Slide 17
Which circuit has the largest 7me constant?
A) Circuit 1
B) Circuit 2
C) Same
CheckPoint 10
Electricity & Magne7sm Lecture 11, Slide 18
CheckPoint 12
Electricity & Magne7sm Lecture 11, Slide 20
ABCDE
0.47 µF Capacitors
Please do not discharge them abruptly through a short.
Put a 10 Ω resistor across the terminals if you wish to discharge them.
Session 3
We don’t have 7me to do session 3 this semester.
Please record BOTH Charge and Discharge curves for your circuit. (Ac7vity 24-‐8)
You can save 7me by figng your data in Logger Pro.
Use the “Analyze” func7on under the menus.
a
RVbattery
C
b
(e) What happens to the potential difference across the
resistor at the same time? Explain.
(f) If the potential across the resistor starts to change what
must happen to the current in the circuit? Explain.
(g) Why does the draining of charge from the capacitor
eventually stop? Why does the current in the circuit go to
zero?
50 min
Capacitor Charging
If the resistor, R, in Figure 24-12 is moved up next to
the battery as shown in Figure 24-13, an uncharged
capacitor, C, can be charged by the battery in the
presence of the resistor. The qualitative and
V
Cq i
i
Two-way!
switch
R
Figure 24-13
quantitative considerations of this situation are very
analogous to that of capacitor decay. For example, the
capacitor charges up more rapidly at first when there
Page 24-26 Workshop Physics II Activity Guide SFU
© 1990-93 Dept. of Physics and Astronomy, Dickinson College Supported by FIPSE (U.S. Dept. of Ed.)
and NSF. Modified at SFU by S. Johnson, 2008.
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