Ohm’s Law
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Transcript of Ohm’s Law
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 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.
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 = 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
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
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
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
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
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