Transcript Ohms Law Ohmic Resistors versus Lightbulbs

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,
V oltage  C urrent  R esistance
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
non-linearly outside of a given range of
temperature, pressure, etc.
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
Parallel Circuit
R total  R  R1  R 2  ...
1
R total

1
R

1
R1

1
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  I 1  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
V in 
 V oltageA crossE achR esistor
V in  V1  V 2  ...
Net Voltage for a circuit = 0
V1
V2
V  V1  V 2
V  V1  V 2  0
V
Series Circuit
Current is constant
• Why?
– Only one path for the
current to take
V  IR
V  V1  V 2  V 3
I  I1  I 2  I 3
R  R1  R 2  R 3
Series Equivalent Circuit
V1  I  R 1
V2  I  R2
V3  I  R3
R  R1  R 2  R 3
V 
V1
 V2

V3
V  I  R1  I  R 2  I  R 3
V  I   R1  R 2  R 3 
V  IR
Parallel Circuit
V  IR
V  V1  V 2  V 3
I  I1  I 2  I 3  I1  I 23
Voltage is constant
w h ere I 2 3  I 2  I 3
• Why?
1
– There are 3 closed
loops in the circuit
R

1
R1

1
R2

1
R3
Parallel Equivalent Circuits
1

R
an d
1

R1
1
R123
1

R2

1
let
R3
1
R1

R3
 1
1 
so



R  R1 R 23 
 R  R123
I  I1  I 2  I 3
1

R 23
1
R 23

1
R
V  I  R   I1  I 2  I 3  
1

R2
1
1
1
1
R1

1
R2

1
R3

I1  I 2  I 3
1
R1

1
R2

1
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
P  I R  V  I 
V
2
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…
R e ca ll: V  I  R  I 
V
R
W h e n w e a d d th e se co n d lig h tb u lb :
V su p p lie d d o e sn 't ch a n g e , b u t R in cre a se s
 I fo r th e circu it d e cre a se s (b u t I1  I 2 )
P  V  I  d e cre a se s
 T h e b u lb s g e t d im m e r
b e ca u se th e p o w e r d issip a te d d e cre a se s
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
R

1
R1

1
R2
Bulbs in parallel experiment
continued…
V  I  R  I 
V
R
P  V  I
1
R

1
R1

1
R2
 R 
1
1
R1

1
R2
V co n sta n t fo r th e circu it, R d e cre a se s  I in cre a se s
 P in cre a se s a s R d e cre a se s
T h e b u lb s d o n o t ch a n g e in b rig h tn e ss,
b u t th e to ta l p o w e r o f th e circu it is in cre a se d
Light bulbs are not linear
• The resistance of light bulbs increases
with temperature


R  Ro  1   T  T o





R  C o n d u cto r re sista n ce a t te m p e ra tu re T [  ]
R o  C o n d u cto r re sista n ce a t re fe re n ce T o [  ]
  T e m p e ra tu re co e fficie n t o f re sista n ce [ C
1
]
T  C o n d u cto r te m p e ra tu re [  C ]
T o  R e fe re n ce te m p e ra tu re  sp e cifie d fo r [ C ]
The filaments of light bulbs are made of Tungsten,
which is a very good conductor. It heats up easily.
 Tu n g sten  0 .0 0 4 4 0 3 / C at 2 0 C (i.e. T o  2 0 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) of bulbs
increases
• 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
R H o t  R C o ld
2
P  I  R  R 

PH o t
I
2

PC o ld
I
2
 PH o t  PC o ld
P
I
2
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
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
Measuring Voltage
Voltage:
Probes connect
to either side of
the resistor
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 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!