Ohm’s Law

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Ohm’s Law Mitsuko J. Osugi Physics 409D Winter 2004 UBC Physics Outreach

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Ohm’s Law. Mitsuko J. Osugi Physics 409D Winter 2004 UBC Physics Outreach. Ohm’s Law. Current through an ideal conductor is proportional to the applied voltage Conductor is also known as a resistor An ideal conductor is a material whose resistance does not change with temperature - PowerPoint PPT Presentation

Transcript of Ohm’s Law

Page 1: Ohm’s Law

Ohm’s Law

Mitsuko J. Osugi

Physics 409DWinter 2004

UBC Physics Outreach

Page 2: Ohm’s Law

Ohm’s LawCurrent through an ideal conductor is

proportional to the applied voltage– Conductor is also known as a resistor– An ideal conductor is a material whose resistance does not change with

temperature

For an ohmic device,

Voltage Current Resistance

V I RV = Voltage V = Voltage (Volts = V)(Volts = V)I = Current I = Current (Amperes = A)(Amperes = A)R = Resistance R = Resistance (Ohms = (Ohms = ΩΩ))

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Current and Voltage DefinedConventional Current: (the current in electrical circuits) Flow of current from positive terminal to the negative

terminal. - has units of Amperes (A) and is measured using ammeters.

Voltage:Energy required to move a charge from one point to another. - has units of Volts (V) and is measured using voltmeters.

Think of voltage as what pushes the electrons along in the circuit, and current as a group of electrons that are constantly trying to reach a state of equilibrium.

Page 4: Ohm’s Law

Ohmic Resistors

• Metals obey Ohm’s Law linearly so long as their temperature is held constant– Their resistance values do not fluctuate with

temperature• i.e. the resistance for each resistor is a constant

Most ohmic resistors will behave non-linearly outside of a given range of temperature, pressure, etc.

Page 5: Ohm’s Law

Voltage and Current Relationship for Linear Resistors

Voltage versus Current for a 10 ohm Resistor

00.10.20.30.40.50.6

0 1 2 3 4 5 6

Voltage (V)

Cu

rre

nt

(A)

Voltage and current are linear when resistance is held constant.

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Ohm’s Law continued

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Ohm’s Law continued

The total resistance of a circuit is dependant on the number of resistors in the circuit and their configuration

1 2

1 2

...

1 1 1 1...

total

total

R R R R

R R R R

Series CircuitSeries Circuit

Parallel CircuitParallel Circuit

Page 8: Ohm’s Law

Kirchhoff’s Current Law

Current into junction = Current leaving junction

in outI I

Iin I1

I2

I2

I1

Iout

1 2

0

in out

in out

I I I I

I I

The amount of current that enters a junction is The amount of current that enters a junction is equivalent to the amount of current that leaves the equivalent to the amount of current that leaves the junctionjunction

Page 9: Ohm’s Law

Kirchhoff’s Voltage Law

Net Voltage for a circuit = 01 2 ...

in

in

V VoltageAcrossEachResistor

V V V

V

V1 V2

Sum of all voltage rises and voltage drops in a circuit (a closed loop) equals zero

1 2

1 2 0

V V V

V V V

Page 10: Ohm’s Law

Series Circuit

Current is constant

• Why?– Only one path for the

current to take

1 2 3

1 2 3

1 2 3

V V V V

I I I I

R R R R

V I R

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Series Equivalent Circuit

1 1 2 2 3 3

1 2 3

1 2 3

1 2 3

1 2 3

V I R V I R V I R

R R R R

V V V V

V I R I R I R

V I R R R

V I R

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Parallel Circuit

1 2 3

1 2 3 1 23

23 2 3

1 2 3

where

1 1 1 1

V V V V

I I I I I I

I I I

R R R R

Voltage is constant

• Why?– There are 3 closed

loops in the circuit

V I R

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Parallel Equivalent Circuits

231 2 3 2 3 1 23

123 1 2 3123 1 23

1 2 31 2 3

1 2 3 1 2 3

1 1 1 1 1 1 1 1 1 1

1 1 1 1

11 1 1 1 1 1

let so

and

R R R R R R R R R R

R R I I I IR R R R

I I IV I R I I I

R R R R R R

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We’ve now looked at how basic electrical circuits work with resistors that obey Ohm’s Law linearly.

We understand quantitatively how these resistors work using the relationship V=IR, but lets see qualitatively using light bulbs.

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The Light Bulb and its Components

• Has two metal contacts at the base which connect to the ends of an electrical circuit

• The metal contacts are attached to two stiff wires, which are attached to a thin metal filament.

• The filament is in the middle of the bulb, held up by a glass mount.

• The wires and the filament are housed in a glass bulb, which is filled with an inert gas, such as argon.

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Light bulbs and Power

Power dissipated by a bulb relates to the brightness of the bulb.

The higher the power, the brighter the bulb. Power is measured in Watts [W]

For example, think of the bulbs you use at home. The 100W bulbs are brighter than the 50W bulbs.

22 V

P I R V IR

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Bulbs in series experiment

One bulb connected to the batteries. Add another bulb to the circuit in series.

Q: When the second bulb is added, will the bulbs become brighter, dimmer, or not change?

• We can use Ohm’s Law to approximate what will happen in the circuit in theory:

V I R

P V I

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Bulbs in series experiment continued…

1 2

Recall:

When we add the second lightbulb:

supplied doesn't change, but increases

for the circuit decreases (but )

decreases

The bulbs get dimmer

because the power dissipated de

VV I R I

R

V R

I I I

P V I

creases

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Bulbs in parallel experimentOne bulb connected to the batteries. Add a second

bulb to the circuit in parallel.

Q: What happens when the second bulb is added?

We can use Ohm’s Law to approximate what will happen in the circuit:

1 2

1 1 1

V I R

P V I

R R R

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Bulbs in parallel experiment continued…

1 2

1 2

1 1 1 11 1

constant for the circuit, decreases increases

increases as R decreases

The bulbs do not change in b

to

rightness,

but the tal power of the circuit is increased

VV I R I

RP V I

RR R R

R R

V R I

P

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Light bulbs are not linear• The resistance of light bulbs increases The resistance of light bulbs increases

with temperaturewith temperature

1

Conductor resistance at temperature [ ]

Conductor resistance at reference [ ]

Temperature coefficient of resistance [ ]

Conductor temperature [ ]

Reference

1

o o

o

R T

R T

o o

C

T C

T

R R T T

temperature specified for [ ]C

The filaments of light bulbs are made of Tungsten, The filaments of light bulbs are made of Tungsten, which is a very good conductor. It heats up easily.which is a very good conductor. It heats up easily.

Tungsten 0.004403 / at 20 (i.e. 20 )oC C T C

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As light bulbs warm up, their resistance increases. If As light bulbs warm up, their resistance increases. If the current through them remains constant:the current through them remains constant:

They glow slightly dimmer when first plugged in.They glow slightly dimmer when first plugged in.

Why?Why?

The bulbs are The bulbs are coolercooler when first plugged in so their when first plugged in so their resistance is lower. As they heat up their resistance resistance is lower. As they heat up their resistance increases but I remains constant increases but I remains constant P increases P increases

Most ohmic resistors will behave non-linearly outside of Most ohmic resistors will behave non-linearly outside of a given range of temperature, pressure, etc.a given range of temperature, pressure, etc.

2P I R

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Voltage versus Current for Constant Resistance

The light bulb does not have a linear relationship. The resistance of the bulb increases as the temperature of the bulb increases.

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“Memory Bulbs” Experiment

• Touch each bulb in succession with the wire, each time completing the series circuit

Q: What is going to happen?

Pay close attention to what happens to each of the bulbs as I close each circuit.

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“Memory Bulbs” Continued…

• Filaments stay hot after having been turned off

• In series, current through each resistor is constant– smallest resistor (coolest bulb) has

least power dissipation, therefore it is the dimmest bulb

22

2 2

Hot Cold

Hot Cold

Hot Cold

R R

PP I R R

IP PI I

P P

How did THAT happen??How did THAT happen??

Temperature of bulbs increases Temperature of bulbs increases resistance increases resistance increases power dissipation (brightness) of bulbs power dissipation (brightness) of bulbs increasesincreases

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Conclusion• Ohmic resistors obey Ohm’s Law linearly

• Resistance is affected by temperature. The resistance of a conductor increases as its temperature increases.

• Light bulbs do not obey Ohm’s Law linearly– As their temperature increases, the power dissipated by

the bulb increases• i.e. They are brighter when they are hotter

V I R