Electricity & Magnetism
Lecture 11
Today’s Concept:
RC Circuits
Electricity & Magne7sm Lecture 11, Slide 1
RC Circuit (Charging)
Capacitor uncharged, Switch is moved to posi?on “a”
aa
C
C
Kirchhoff’s Voltage Rule
battery
VV
battery
bb
RR
Short Term (q = q0 = 0)
Intermediate
Long Term (Ic = 0)
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 = V
B) V1 = 0
C) V1 = 0
V2 = V
V2 = 0
D) V1 = V
V2 = 0
Electricity & Magne7sm Lecture 11, Slide 3
RC Circuit (Discharging)
Capacitor has q0 = CV, Switch is moved to posi?on “b”
Kirchhoff’s Voltage Rule
aa
C
C
+ −
Vbattery
Vbattery
bb
I
RR
Short Term (q = q0)
Intermediate
V
Long Term (Ic = 0)
−I
Electricity & Magne7sm Lecture 11, Slide 4
CheckPoint 6
+
−
A
B
C
D
Electricity & Magne7sm Lecture 11, Slide 5
CheckPoint 8
A
B
C
Electricity & Magne7sm Lecture 11, Slide 6
DEMO – Clicker Question 1
Bulb 2
S
V
Bulb 1
R
R
C
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.
Electricity & Magne7sm Lecture 11, Slide 8
DEMO – Clicker Question 2
Bulb 2
S
V
Bulb 1
R
R
C
Suppose the switch has been closed a long ?me.
Now what will happen aFer open the switch?
A)
B)
C)
D)
Both bulbs come on and stay on.
Both bulbs come on but then bulb 2 fades out.
Both bulbs come on but then bulb 1 fades out.
Both bulbs come on and then both fade out.
Electricity & Magne7sm Lecture 11, Slide 9
Calculation
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 Analysis
Determine currents and voltages in circuit a long 7me a@er S closed
Electricity & Magne7sm Lecture 11, Slide 10
Calculation
S
R1
R2
C
V
R3
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 ?
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
Electricity & Magne7sm Lecture 11, Slide 11
Calculation
I1
S
R1
V
R2
C
R3
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 ?
Immediately a@er S is closed, what is I1, the current through R1 ?
A B C D E
Electricity & Magne7sm Lecture 11, Slide 12
Calculation
S
R1
V
R2
C
R3
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 ?
A@er S has been closed “for a long 7me”, what is IC, the current through C ?
A B C
Electricity & Magne7sm Lecture 11, Slide 13
Calculation
R1
V
S
R2
C
R3
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 ?
A@er S has been closed “for a long 7me”, what is VC, the voltage across C ?
A B C D E
Electricity & Magne7sm Lecture 11, Slide 14
How do Exponentials Work?
Q(t) = Q0 e
t/RC
1.0000
0.7500
“Frac?on of ini?al charge that remains”
0.5000
0.2500
0
0
2.5000
5.0000
7.5000
10.0000
“How many ?me constants worth of ?me that have elapsed”
Electricity & Magne7sm Lecture 11, Slide 16
Q(t) = Q0 e
t/RC
1.0000
0.7500
0.5000
Time constant:
τ = RC
The bigger τ is,
the longer it takes to get
the same change…
RC = 2
0.2500
RC = 1
0
0
2.5000
5.0000
7.5000
10.0000
Electricity & Magne7sm Lecture 11, Slide 17
CheckPoint 10
Which circuit has the largest 7me constant?
A)
Circuit 1
B)
Circuit 2
C)
Same
Electricity & Magne7sm Lecture 11, Slide 18
CheckPoint 12
A
B
C
D
E
Electricity & Magne7sm Lecture 11, Slide 20
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
(g) Why does the draining of charge from the ca
eventually stop? Why does the current in the ci
zero?
We don’t have 7me to do session 3 this semester.
50 min
Capacitor Charging
If the resistor, R, in Figure 24-12 is moved u
the battery as shown in Figure 24-13, an un
capacitor, C, can be charged by the battery
presence of the resistor. The qualitative and
Please record BOTH Charge and Discharge curves for your circuit. (Ac7vity 24-­‐8)
a
R
C
Text
Use this
Vbattery
q
b
R
C
V
i
Instead of this
Two-way
switch
i
Figure 24-13
quantitative considerations of this situation
analogous to that of capacitor decay. For ex
capacitor charges up more rapidly at first w
You can save 7me by figng your data in Logger Pro.
Use the “Analyze” func7on under the menus.
© 1990-93 Dept. of Physics and Astronomy, Dickinson College Supported by FIPSE (U.
and NSF. Modified at SFU by S. Johnson, 2008.