Physics 1809: Resistors, Capacitors, and RC Circuits Purpose of this Minilab Learn about charging and discharging of a capacitor through a resistor. Learn.

Physics 1809: 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”.


What is a “Capacitor”?

Capacitor = an object that can store electric charge Q.

Example: Two metal plates

++

+

++ ++

+--

--

--

--


What is a “Capacitor”?

Relationship between charge and voltage

++

+

++ ++

+--

--

--

--

Total charge on one plate: Q

Voltage V

VCQ

Capacitanceof the capacitor


Getting the Charge on the Capacitor

Current (movement of charge) must occur: Applying a voltage willcause current to flow when switch is closed.

battery/power supply

switch

e

not charged…yet

resistance of circuitR

C



++

+

+

-

--

-

e

I I

I I Current decreasesas charge increaseson the capacitor.

Voltage across capacitor is increasing as more charge is deposited.

C

QVcapacitor

has opposite polaritycompared to e.

capacitorV



++

+

+

-

--

-

e

I = 0

Capacitor is fully charged No more current flows

capacitorV capacitorV

+++

+-

-

-

-


The Charging Process …Mathematically

I

RC

t

eR

I

t

V

RC

t

eCQ 1

t

Q

RC

t

eC

QV 1


Discharging the Capacitor

++

+

+

-

--

-

I I

I I Current decreasesas charge decreaseson the capacitor.

Voltage across capacitor is decreasing as charge is leaving.

capacitorV

Removing battery and closing the loop:


The Discharging Process …Mathematically

I

RC

t

eR

I

t

V

RC

t

eCQ

t

Q

RC

t

eC

QV

Note: Current flows inopposite directioncompared to charging.


The “RC time constant”

The product RC has units of time: It is called the “time constant of the RC circuit”.

RC

t

capacitor etV

)(

For the discharging process we saw:

initial voltage of the capacitor at time t=0 (start of discharge)

so…after a time t=RC has elapsed…..

3678.0)( 1 eeV RC

RC

RCtcapacitor


Measuring the “RC time constant” During the Discharge Process

V

t

Vinitial

Vinitial*0.368

RC

Note: Your initial voltage can be at ANY starting point.


The “RC time constant”

For the charging process we saw:

and…after a time t=RC has elapsed…..

6322.011)( 1

eeV RC

RC

RCtcapacitor

RC

t

etV 1)( 0)( 0 tV

And the final (maximum) voltage is reached after a “long” time…

011)( eeV RCtcapacitor


Measuring the “RC time constant” During the Charging Process

Vcapacitor

t

Vfinal

Vfinal*0.63

RC

Note: Your initial voltage must be 0.


Using the Function Generator to Automate Charging and Discharging

V

Must use the square wave of function generator

CR


Measuring Vcapacitor(t) with the Oscilloscope

V

CR

Oscilloscope


Connections

CR

Oscilloscope

FunctionGenerator

The black cables clipsmust be located as shown!


Power remains OFF on breadboard in this lab.

ToOscilloscope

ToFunctionGenerator


Capacitor

Resistor

To FunctionGenerator

Both black clipsmust be attachedto the same pointin circuit.

To OscilloscopeA Close View


Choosing a Good Frequency on Function Generator

FunctionGeneratorVoltage

time

Capacitorcharges

Capacitordischarges

Capacitorcharges

Capacitordischarges

Theoretical charge time = RCPeriod (T) should be approximately 10*RC so that capacitor can fully charge and discharge.frequency (=1/T) should be approximately 1/(10*RC)

Period (T)


If Frequency is Chosen Well ….Oscilloscope Will Show ….

Oscilloscope(Vcapacitor)

time

Capacitorcharges

Capacitordischarges

Capacitorcharges

Capacitordischarges


Frequency too High …..


time

Not enough time for proper charging and discharging: Looks like sawtooth


Frequency too Low Harder to Measure RC


time

Capacitorcharges

Capacitordischarges

Capacitorcharges

Capacitordischarges


Choose Oscilloscope Channel 1 Mode = DC

First push “Ch1 Menu” Button

Then select coupling With this button (must be “DC”).


Hints for Measuring RC with Oscilloscope

* Use the cursor functions to measure voltages and time differences.* Expand x and y axes to get good resolution.

Vmax0.63 Vmax

RC


The Capacitance Meter

Small knob canbe turned to “zero” capacitancemeter.


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.


Using Capacitance Meter without Clips

1) Remove leads.

2) “Zero” capacitance meter without capacitor attached.

3) Insert capacitor into slits as shown.


Making a Resistor from Paper and Carbon

White cardboard

Draw with pencil(apply thick layer).

Use alligator clipsto make goodelectric contact.


Measuring R

If you deposit a generousthickness of carbon, aboutas large as shown, you shouldget approx. 100kW resistance.

If you get a few MW, you needto apply carbon more thicklywith the pencil.


Varying Length (L) and Area (A) of Resistor

L

A

LR

Simply attach clips at different positions to vary L.

W

Varying W effectivelychanges A (A=W*Thickness of carbon) Draw broader W for more A.


Making a Capacitor

8”x11” paper

Leave overhang for clips

Aluminum foil smaller thanpaper (but not much smaller).Keep Aluminum foil as flat aspossible.


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.


Varying the Capacitance

d

AC

Area of capacitor (in ourcase this is the area of overlap of the two aluminum foils).

Distance between the aluminum foils( = thickness of paper).


Varying the Capacitance

d

AC

Change “d” by inserting 1, 2, 3…sheets of paper between the twofoils (doubles, triples, etc. “d”).

You can simply move one sheet tochange the area of overlap.

Effective area of overlap.

Make sure to cover with book again!!

Physics 1809: Resistors, Capacitors, and RC Circuits Purpose of this Minilab Learn about charging and discharging of a capacitor through a resistor. Learn.

Documents

capacitor slide

rc note

rc circuits purpose

rc time constant

product rc

t v t q slide

time t

long time slide