Electrical Circuits

Topics

• Flow of Charge• Electric Current• Voltage Sources• Electrical Resistance• Ohm’s Law• Direct Current and Alternating Current• Speed and Source of Electrons in a Circuit• Electric Power• Electric Circuits

Electric Charges

Electric Charges

Would this work?

Would this work?

Batteries and Bulbs

• Would this work?

A “Current” flowing through a loop

Electric Fields in Circuits

• Point away from positive terminal, towards negative• Channeled by conductor (wire)• Electrons flow opposite field lines (neg. charge)

E

E

E

electrons & direction of motion

E Electric field direction

Batteries produce a voltage

• Typical Alkaline cells produce 1.5 Volts– AAA cells

– AA cells

– D cells

• Putting batteries in series, voltages add• Putting batteries in parallel, same voltage as a single cell, but can draw

more current, lasts longer (more water in reservoir)

Electric Charges

Electric Charges

Relationship between Voltage, Current and Resistance: Ohm’s Law

• There is a simple relationship between voltage, current and resistance:

V is in Volts (V)I is in Amperes, or amps (A)R is in Ohms ()

V = I R

Ohm’s Law

V I R

Examples

• What is the ratio of the currents that flow in these 2 circuits?

4 V 10 Ohms 8 V 20 Ohms

Class Problem - Ohm’s Law (V = I·R)

• How much voltage is being supplied to a circuit that contains a 1 Ohm resistance, if the current that flows is 1.5 Amperes?

• If a 12 Volt car battery is powering headlights that draw 0.5 Amps of current, what is the total resistance in the circuit?

Class Problem

(How much voltage is being supplied to a circuit that contains a 1 Ohm resistance, if the current that flows is 1.5 Amperes?)

• Use the relationship between Voltage, Current and Resistance, V = IR.

• Total resistance is 1 Ohm• Current is 1.5 Amps

So V = IR = (1.5 Amps)(1 Ohms) = 1.5 Volts

Class Problem

If a 12 Volt car battery is powering headlights that draw 0.5 Amps of current, what is the total resistance in the circuit?

• Again need V = IR• Know I, V, need R• Rearrange equation: R = V divided by I

= (12 Volts)/(0.5 Amps)

= 24 Ohms

How about multiple resistances?• Resistances in series simply add• Voltage across each one is V = IR

Total resistance is 10 + 20 = 30 So current that flows must be I = V/R = 3.0 V / 30 = 0.1 AWhat are the Voltages across R1 and R2?

R1=10 R2=20

V = 3.0 Volts

Voltage is potential, bulb presents resistance

• Battery is like reservoir of elevated water– The higher, the bigger the potential, or voltage

• Imagine bulbs as small tubes that let water drain– Resistance is represented by length of tube

shorter: less resistance: more current flows

longer: more resistance: less current flows

Voltage

Parallel Resistances are a little trickier....

• Rule for resistances in parallel:

1/Rtot = 1/R1 + 1/R2

10 Ohms 10 Ohms 5 Ohms

Can arrive at this by applying Ohm’s Law to find equal currentin each leg. To get twice the current of a single10 , could use 5 .

Water Analogy

Voltage

A

BA

B

side view

A

Bside view

CVoltage B+C

A

Power Dissipation

• Physical model – electrons bumping into things! • Kinetic Energy is turned into thermal energy (heat)• Power = Voltage Current• P = V I

A device with a voltage drop of 1 Volt that passes a current of 1 Amp uses 1 Watt of power.

Multi-bulb circuits

Rank the expected brightness of the bulbs in the circuits shown, e.g. A>B, C=B, etc. WHY?!

A

+_

B

C

+_

Answer:

• Bulbs B and C have the same brightness, since the same current is flowing through them both.

• Bulb A is brighter than B and C are, since there is less total resistance in the single-bulb loop, so

A > B=C.

Adding Bulbs

• Where should we add bulb C in order to get A to shine more brightly?

C

A

B

+_

Answer

• The only way to get bulb A to shine more brightly is to increase the current flowing through A.

• The only way to increase the current flowing through A is to decrease the total resistance in the circuit loop

• Since bulbs in parallel produce more paths for the current to take, the best (and only) choice for C is to put it in parallel with B, as illustrated on next page

How to get A to shine more brightly:

A

B

+_

C

Phet

http:phet.colorado.edu/simulations/sims.php?sim=Circuit_Construction_Kit_DC_Only

Exercises

If you double the voltage across a light bulb, while keeping the current the same, by what factor does the power consumption increase?

If you double the current through a resistor, by what factor does the consumption change?

Answers

• If you double the voltage while keeping the current fixed, the power consumption doublesP = IV

• If you double the current though a resistor, the power used goes up by a factor of 4! This is because both the current and the voltage doubleP = I V = I (IR) = I2 R

Flashlights

• “A holder for dead batteries”• How does a flashlight work?

– Light source?

– Power source?

– Control device?

Incandescent Bulb

Electrical contacts

Tungsten Filament

Sealed Bulb

120 W bulb at 120 V must be conducting 1 Amp (P = VI)Bulb resistance is then about 120 Ohms (V = IR)

What limits bulb’s lifetime?

• Heated tungsten filament drives off tungsten atoms• Tradeoff between filament temperature and lifetime

– Eventually the filament burns out, and current no longer flows – no more light!

• How “efficient” do you think incandescent bulbs are?

Efficiency

• Ratio between energy doing what you want vs. energy supplied

Efficiency = (energy emitted as visible light)/(total supplied)

For incandescent bulbs, efficiency is at most 10% percent– Where does the rest of the energy go?

Decorative Lights

• Strings of lights used to decorate contain many bulbs• In some light sets, a single bulb going out can shut off the entire

set– How do you think sets like this are wired up?

• How might you design a light set that still works, even if a bulb goes out?

Series combo: one goesno light

Fault-tolerant light sets

1. Wire up the bulbs in parallel, then if one goes out it still works

Lights in your Car

• The car has a battery as part of its electrical system– (as well as a generator, voltage regulator, etc..)

• Lights in a car include:– Interior light, turn on when the door opens

– Turn signals

– Brake lights

– Headlights (high and low beam)

• The illustrations that follow are by no means the only way to accomplish these tasks!

Brake lights

Pedal Switch

Plus red filter to get desired color

Interior car lights

Doorswitch

Manual Switch

Switches wired in parallel: either one will do!(Example of OR logic circuit)

Class Problem• The simple series circuit consists of three identical lamps powered by battery. When a wire is

connected between points a and b,

a) What happens to the brightness of lamp 3?

b) Does current in the circuit increase, decrease or remain the same?

c) What happens to the brightness of lamps 1 and 2?

d) Does the voltage drop across lamps 1 and 2 increase, decrease, or remain the same?

e) Is the power dissipated by the circuit increased, decreased, or does it remain the same?

Class Problem• a) Lamp 3 is short-circuited. It no longer glows because no current passes through it.

b) The current in the circuit increases. Why? Because the circuit resistance is reduced. Whereas charge was made to flow through three lamps before, now it flows through only two lamps. So more energy is now given to each lamp.

c) Lamps 1 and 2 glow brighter because of the increased current through them.

d) The voltage drop across lamps 1 and 2 is greater. Whereas voltage supplied by the battery was previously divided between three lamps, it is now divided only between two lamps. So more energy is now given to each lamp.

e) The power output of the two-lamp circuit is greater because of the greater current. This means more light will be emitted by the two lamps in series than from the three lamps in series. Three lamps connected in parallel, however, put out more light. Lamps are most often connected in parallel.