Ohm’s Law

Mitsuko J. Osugi

Physics 409DWinter 2004

UBC Physics Outreach

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))

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.

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.

Voltage and Current Relationship for Linear Resistors

Voltage and current are linear when resistance is held constant.

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)

Ohm’s Law continued

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

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

Kirchhoff’s Voltage Law

Net Voltage for a circuit = 0

1 2 ...

in

in

V VoltageAcrossEachResistor

V V V

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

V

V1 V2

1 2

1 2 0

V V V

V V V

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

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

Parallel Circuit

Voltage is constant

• Why?– There are 3 closed

loops in the 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

V I R

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

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.

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.

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

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

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

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

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

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

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

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.

“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.

“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

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

22

2 2

Hot Cold

Hot Cold

Hot Cold

R R

PP I R R

IP PI I

P P

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

You’re turn to do some experiments!

Now you get to try some experiments of your own, but first, a quick tutorial on the equipment you will be using

The equipment you’ll be using:

- Voltmeter

- Breadboard

- Resistors

- 9V battery

Let’s do a quick review…

How to use a voltmeter:

Voltmeter: - connect either end of the meter to each side of

the resistor

If you are reading a negative value, you have the probes switched.

There should be no continuity beeping. If you hear beeping, STOP what you are doing and ask someone for help!

Voltmeter

Voltage:

Probes connect to either side of the resistor

Measuring Voltage

Breadboards• You encountered breadboards early in the

year. Let’s review them:

The breadboard

How the holes on the top of the board are connected:

Series

Resistors are connected such that the current can only take one path

Parallel

Resistors are connected such that the current can take multiple paths

Real dataReal data

In reality, the data we get is not the same as what we get in theory.

Why?

Because when we calculate numbers in theory, we are dealing with an ideal system. In reality there are sources of error in every aspect, which make our numbers imperfect.

Now go have fun!