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
For an ohmic device,
Voltage  Current  Resistance
V  I R
V = Voltage
I = Current
R = Resistance
(Volts = V)
(Amperes = A)
(Ohms = Ω)
Current and Voltage Defined
Conventional 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
linearly outside of a given range of
temperature, pressure, etc.
non-
Voltage and Current Relationship for
Linear Resistors
Current (A)
Voltage versus Current
for a 10 ohm Resistor
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
Voltage (V)
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
Series Circuit
Rtotal  R  R1  R2  ...
Parallel Circuit
1
1 1 1
  
 ...
Rtotal R R1 R2
Kirchhoff’s Current Law
Current into junction = Current leaving junction
I in  I out
The amount of current that enters a junction is
equivalent to the amount of current that leaves the
junction
Iin
I1
I1
I2
I2
Iout
I in  I1  I 2  I out
I in  I out  0
Kirchhoff’s Voltage Law
Sum of all voltage rises and voltage drops
in a circuit (a closed loop) equals zero
Vin  VoltageAcrossEachResistor
Vin  V1  V2  ...
Net Voltage for a circuit = 0
V1
V2
V  V1  V2
V  V1  V2  0
V
Series Circuit
Current is constant
• Why?
– Only one path for the
current to take
V  I R
V  V1  V2  V3
I  I1  I 2  I 3
R  R1  R2  R3
Series Equivalent Circuit
V1  I  R1 V2  I  R2 V3  I  R3
R  R1  R2  R3
V
V1  V2  V3
V  I  R1  I  R2  I  R3
V  I   R1  R2  R3 
V  IR
Parallel Circuit
V  I R
V  V1  V2  V3
I  I1  I 2  I 3  I1  I 23
Voltage is constant
where I 23  I 2  I 3
• Why?
1 1
1
1
 

R R1 R2 R3
– There are 3 closed
loops in the circuit
Parallel Equivalent Circuits
1 1
1
1
1
1
1
1 1
1 
 

let


so   

R R1 R2 R3
R 23 R2 R3
R  R1 R23 
1
1
1
1
and
 
  R  R123
I  I1  I 2  I 3
R123 R1 R23 R
I1  I 2  I 3
1
V  I  R   I1  I 2  I 3  

1
1
1
1
1
1




R1 R2 R3 R1 R2 R3
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]
2
V
P  I2  R  V  I 
R
For example, think of the bulbs you use at home. The
100W bulbs are brighter than the 50W bulbs.
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…
V
Recall:V  I  R  I 
R
When we add the second lightbulb:
V supplied doesn't change, but R increases
 I for the circuit decreases (but I1  I2 )
P  V  I  decreases
 The bulbs get dimmer
because the power dissipated decreases
Bulbs in parallel experiment
One 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:
V  IR
P V I
1
1
1


R R1 R2
Bulbs in parallel experiment
continued…
V
V  IR I 
R
P V I
1
1
1
1


R
1
1
R R1 R2

R1 R2
V constant for the circuit, R decreases  I increases
 P increases as R decreases
The bulbs do not change in brightness,
but the total power of the circuit is increased
Light bulbs are not linear
• The resistance of light bulbs increases
with temperature

R  Ro  1   T  To





R  Conductor resistance at temperature T []
Ro  Conductor resistance at reference To []
  Temperature coefficient of resistance [C 1]
T  Conductor temperature [C ]
To  Reference temperature  specified for [C ]
The filaments of light bulbs are made of Tungsten,
which is a very good conductor. It heats up easily.
 Tungsten  0.004403 / C at 20C (i.e. To  20C )
As light bulbs warm up, their resistance increases.
If the current through them remains constant:
2
P  I R
They glow slightly dimmer when first plugged in.
Why?
The bulbs are cooler when first plugged in so their
resistance is lower. As they heat up their resistance
increases but I remains constant  P increases
Most ohmic resistors will behave non-linearly outside of
a given range of temperature, pressure, etc.
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…
How did THAT happen??
Temperature of bulbs increases
 resistance increases
 power dissipation (brightness) ofR bulbs
R
increases
P
P  I R  R 
I
P
P
• Filaments stay hot after having


I
I
been turned off
P  P
• In series, current through each
resistor is constant
Hot
Cold
2
2
Hot
2
Hot
– smallest resistor (coolest bulb) has
least power dissipation, therefore it
is the dimmest bulb
Cold
2
Cold
Conclusion
• Ohmic resistors obey Ohm’s Law linearly
V  IR
• 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