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Resistors, Capacitors, and RC Circuits
Purpose of this Minilab
• Learn about charging and discharging of a capacitor
through a resistor.
• Learn how to build a simple resistor and capacitor
from
“everyday materials”.
Resistors, Capacitors, and RC Circuits
What is a “Capacitor”?
Capacitor = an object that can store electric charge Q.
Example: Two metal plates
+
+
+
+
+
+ +
+
- - --
Resistors, Capacitors, and RC Circuits
What is a “Capacitor”?
Relationship between charge and voltage
Total charge on one plate: Q
+
+
+
+
+
+ +
+
- - -Voltage V
Q  CV
Capacitance
of the capacitor
Resistors, Capacitors, and RC Circuits
Getting the Charge on the Capacitor
Current (movement of charge) must occur: Applying a voltage will
cause current to flow when switch is closed.
C
switch
not charged…yet
battery/power supply
R
e
resistance of circuit
Resistors, Capacitors, and RC Circuits
Getting the Charge on the Capacitor
Voltage across capacitor is increasing as
more charge is deposited.
Q
Vcapacitor 
C
Vcapacitor
has opposite polarity
compared to e.
+
+
+
I
+
I
- -
I
I
e
Current decreases
as charge increases
on the capacitor.
Resistors, Capacitors, and RC Circuits
Getting the Charge on the Capacitor
Vcapacitor   e
Vcapacitor
+
+
+
++
+ +
+
I=0
e
- - -
Capacitor is fully charged
 No more current flows
Resistors, Capacitors, and RC Circuits
The Charging Process …Mathematically
I
I
e
R
e

t
RC
t
Q
V
t



RC 

Q  Ce 1  e 


t



Q
RC 

V   e 1  e 
C


t
Resistors, Capacitors, and RC Circuits
Discharging the Capacitor
Removing battery and closing the loop:
Voltage across capacitor is decreasing as charge is leaving.
Vcapacitor
+
+
+
I
+
I
- -
I
I
Current decreases
as charge decreases
on the capacitor.
Resistors, Capacitors, and RC Circuits
The Discharging Process …Mathematically
I
Note: Current flows in
opposite direction
compared to charging.
I
e
R
e

t
RC
t
Q
Q  Cee

t
RC
V
t

Q
V   ee RC
C
t
Resistors, Capacitors, and RC Circuits
The “RC time constant”
The product RC has units of time:
It is called the “time constant of the RC circuit”.
For the discharging process we saw:
Vcapacitor(t )  e e

t
RC
initial voltage of the capacitor at time t=0 (start of discharge)
so…after a time t=RC has elapsed…..
Vcapacitor(t  RC )  e e

RC
RC
 e e 1  0.3678 e
Resistors, Capacitors, and RC Circuits
Measuring the “RC time constant” During
the Discharge Process
V
Vinitial
Vinitial*0.368
t
RC
Note: Your initial voltage can be at ANY starting point.
Resistors, Capacitors, and RC Circuits
The “RC time constant”
For the charging process we saw:
t



RC
V (t )  e 1  e 



V (t  0)  0
and…after a time t=RC has elapsed…..
RC



RC
Vcapacitor(t  RC)  e 1  e   e 1  e 1  0.6322 e




And the final (maximum) voltage is reached after a “long” time…




RC
Vcapacitor(t  )  e 1  e   e 1  e 0  e




Resistors, Capacitors, and RC Circuits
Measuring the “RC time constant” During
the Charging Process
Vcapacitor
Vfinal
Vfinal*0.63
RC
Note: Your initial voltage must be 0.
t
Resistors, Capacitors, and RC Circuits
Using the Function Generator to Automate
Charging and Discharging
C
R
V
Must use the square wave of function generator
Resistors, Capacitors, and RC Circuits
Measuring Vcapacitor(t) with the Oscilloscope
Oscilloscope
C
R
V
Resistors, Capacitors, and RC Circuits
Connections
Oscilloscope
C
R
The black cables clips
must be located as
shown!
Function
Generator
Resistors, Capacitors, and RC Circuits
Power remains OFF on breadboard in this lab.
To
Oscilloscope
To
Function
Generator
Resistors, Capacitors, and RC Circuits
A Close View
To Oscilloscope
Capacitor
Resistor
Both black clips
must be attached
to the same point
in circuit.
To Function
Generator
Resistors, Capacitors, and RC Circuits
Choosing a Good Frequency on Function Generator
Period (T)
Function
Generator
Voltage
time
Capacitor Capacitor Capacitor Capacitor
charges dischargescharges discharges
Theoretical charge time = RC
Period (T) should be approximately 10*RC so that capacitor
can fully charge and discharge.
frequency (=1/T) should be approximately 1/(10*RC)
Resistors, Capacitors, and RC Circuits
If Frequency is Chosen Well ….
Oscilloscope Will Show ….
Oscilloscope
(Vcapacitor)
time
Capacitor Capacitor Capacitor Capacitor
charges discharges charges discharges
Resistors, Capacitors, and RC Circuits
Frequency too High …..
Oscilloscope
(Vcapacitor)
time
Not enough time for proper charging and discharging:
 Looks like sawtooth
Resistors, Capacitors, and RC Circuits
Frequency too Low  Harder to Measure RC
Oscilloscope
(Vcapacitor)
time
Capacitor Capacitor Capacitor Capacitor
charges discharges charges discharges
Resistors, Capacitors, and RC Circuits
Choose Oscilloscope Channel 1 Mode = DC
First push “Ch1 Menu” Button
Then select coupling
With this button
(must be “DC”).
Resistors, Capacitors, and RC Circuits
Hints for Measuring RC with Oscilloscope
* Use the cursor functions to measure voltages and time differen
* Expand x and y axes to get good resolution.
0.63 Vmax
RC
Vmax
Resistors, Capacitors, and RC Circuits
The Capacitance Meter
Small knob can
be turned to
“zero” capacitance
meter.
Resistors, Capacitors, and RC Circuits
Using Capacitance Meter with Clips
1) First position leads
where you want them.
2) “Zero” capacitance
meter without
capacitor attached.
3) Attach capacitor but
try to move leads as
little as possible.
Resistors, Capacitors, and RC Circuits
Using Capacitance Meter without Clips
1) Remove leads.
2) “Zero” capacitance
meter without
capacitor attached.
3) Insert capacitor into
slits as shown.
Resistors, Capacitors, and RC Circuits
Making a Resistor from Paper and Carbon
White cardboard
Use alligator clips
to make good
electric contact.
Draw with pencil
(apply thick layer).
Resistors, Capacitors, and RC Circuits
Measuring R
If you deposit a generous
thickness of carbon, about
as large as shown, you should
get approx. 100kW resistance.
If you get a few MW, you need
to apply carbon more thickly
with the pencil.
Resistors, Capacitors, and RC Circuits
Varying Length (L) and Area (A) of Resistor
L
R
A
L
W
Simply attach clips
at
different positions
to
vary L.
Varying W effectively
changes A
(A=W*Thickness of carbon)
 Draw broader W for
more A.
Resistors, Capacitors, and RC Circuits
Making a Capacitor
8”x11” paper
Aluminum foil smaller than
paper (but not much smaller).
Keep Aluminum foil as flat as
possible.
Leave overhang for clips
Resistors, Capacitors, and RC Circuits
Step-by-Step
1
2
3
4
5
The two aluminum foils must not touch each other anywhere.
(Separate them with a sheet of paper).
Put a heavy book on top to keep aluminum foil as flat as possible.
Use the overhangs to make electric connection with alligator clips.
Resistors, Capacitors, and RC Circuits
Varying the Capacitance
A
C e
d
Area of capacitor (in our
case this is the area of overlap
of the two aluminum foils).
Distance between the aluminum foils
( = thickness of paper).
Resistors, Capacitors, and RC Circuits
Varying the Capacitance
A
C e
d
Change “d” by inserting 1, 2, 3…
sheets of paper between the two
foils (doubles, triples, etc. “d”).
You can simply move one sheet to
change the area of overlap.
Effective area of overlap.
Make sure to cover with book again!!