Purpose of this Minilab

Physics 2225 : 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”.

Physics 2225 : Resistors, Capacitors, and RC Circuits

What is a “Capacitor”?

Capacitor = an object that can store electric charge Q.

Example: Two metal plates

++

+

++ ++

+--

--

----

Physics 2225 : Resistors, Capacitors, and RC Circuits

What is a “Capacitor”?

Relationship between charge and voltage

++

+

++ ++

+--

--

---

-

Total charge on one plate: Q

Voltage V

VCQ

Capacitanceof the capacitor

Physics 2225 : Resistors, Capacitors, and RC Circuits

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

Physics 2225 : Resistors, Capacitors, and RC Circuits

Getting the Charge on the Capacitor

++

+

+

-

---

e

I I

I I Current decreasesas charge increaseson the capacitor.

Voltage across capacitor is increasing as more charge is deposited.

CQVcapacitor

has opposite polaritycompared to e.

capacitorV

Physics 2225 : Resistors, Capacitors, and RC Circuits

Getting the Charge on the Capacitor

++

+

+

-

---

e

I = 0

Capacitor is fully charged No more current flows

capacitorV ecapacitorV

+++

+ -

-

-

-

Physics 2225 : Resistors, Capacitors, and RC Circuits

The Charging Process …MathematicallyI

RCt

eR

I

e

t

V

RCt

eCQ 1e

t

Q

RCt

eCQV 1e

Physics 2225 : Resistors, Capacitors, and RC Circuits

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:

Physics 2225 : Resistors, Capacitors, and RC Circuits

The Discharging Process …MathematicallyI

RCt

eR

I

e

t

V

RCt

eCQ

e

t

Q

RCt

eCQV

e

Note: Current flows inopposite directioncompared to charging.

Physics 2225 : 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”.

RCt

capacitor etV

e)(

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…..

eee 3678.0)( 1 eeV RC

RC

RCtcapacitor

Physics 2225 : Resistors, Capacitors, and RC Circuits

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.

Physics 2225 : Resistors, Capacitors, and RC Circuits

The “RC time constant”

For the charging process we saw:

and…after a time t=RC has elapsed…..

eee 6322.011)( 1

eeV RCRC

RCtcapacitor

RCt

etV 1)( e 0)( 0 tV

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

eee

011)( eeV RCtcapacitor

Physics 2225 : Resistors, Capacitors, and RC Circuits

Measuring the “RC time constant” During the Charging Process

Vcapacitor

t

Vfinal

Vfinal*0.63

RC

Note: Your initial voltage must be 0.

Physics 2225 : Resistors, Capacitors, and RC Circuits

Using the Function Generator to Automate Charging and Discharging

V

Must use the square wave of function generator

CR

Physics 2225 : Resistors, Capacitors, and RC Circuits

Measuring Vcapacitor(t) with the Oscilloscope

V

CR

Oscilloscope

Physics 2225 : Resistors, Capacitors, and RC Circuits

Connections

CR

Oscilloscope

FunctionGenerator

The black cables clipsmust be located as shown!

Physics 2225 : Resistors, Capacitors, and RC Circuits

Power remains OFF on breadboard in this lab.

ToOscilloscope

ToFunctionGenerator

Physics 2225 : Resistors, Capacitors, and RC Circuits

Capacitor

Resistor

To FunctionGenerator

Both black clipsmust be attachedto the same pointin circuit.

To OscilloscopeA Close View

Physics 2225 : Resistors, Capacitors, and RC Circuits

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)

Physics 2225 : Resistors, Capacitors, and RC Circuits

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

Oscilloscope(Vcapacitor)

time

Capacitorcharges

Capacitordischarges

Capacitorcharges

Capacitordischarges

Physics 2225 : Resistors, Capacitors, and RC Circuits

Frequency too High …..

Oscilloscope(Vcapacitor)

time

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

Physics 2225 : Resistors, Capacitors, and RC Circuits

Frequency too Low Harder to Measure RC

Oscilloscope(Vcapacitor)

time

Capacitorcharges

Capacitordischarges

Capacitorcharges

Capacitordischarges

Physics 2225 : 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”).

Physics 2225 : Resistors, Capacitors, and RC Circuits

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

Physics 2225 : Resistors, Capacitors, and RC Circuits

The Capacitance Meter

Small knob canbe turned to “zero” capacitancemeter.

Physics 2225 : 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.

Physics 2225 : 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.

Physics 2225 : Resistors, Capacitors, and RC Circuits

Making a Resistor from Paper and Carbon

White cardboard

Draw with pencil(apply thick layer).

Use alligator clipsto make goodelectric contact.

Physics 2225 : Resistors, Capacitors, and RC Circuits

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.

Physics 2225 : Resistors, Capacitors, and RC Circuits

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

LALR

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.

Physics 2225 : Resistors, Capacitors, and RC Circuits

Making a Capacitor

8”x11” paper

Leave overhang for clips

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

Physics 2225 : 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.

Physics 2225 : Resistors, Capacitors, and RC Circuits

Varying the Capacitance

dAC e

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

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

Physics 2225 : Resistors, Capacitors, and RC Circuits

Varying the Capacitance

dAC e

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!!