This document provides an overview of Ohm's law and basic circuit concepts. It begins by defining Ohm's law, which states that current through a conductor is directly proportional to the voltage applied. It then discusses how voltage and current are defined, and how resistors obey Ohm's law linearly only within a certain temperature range. The document explains series and parallel circuits, and how their current and voltage behaviors can be modeled. It concludes by discussing how light bulbs are non-ohmic resistors whose resistance increases with temperature.

1. Ohm’s Law

2. 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 (Volts = V)
I = Current (Amperes = A)
R = Resistance (Ohms = Ω)

3. 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.

4. 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.

5. Voltage and Current Relationship for Linear Resistors
Voltage and current are linear when resistance is held constant.
Voltage versus Current for a 10 ohm Resistor00.10.20.30.40.50.60123456Voltage (V) Current (A)

6. Ohm’s Law continued

7. 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 Circuit
Parallel Circuit

8. Kirchhoff’s Current Law
Current into junction = Current leaving junction
 in out I 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
equivalent to the amount of current that leaves the
junction

9. 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

10. Series Circuit
Current is constant
•Why?
–Only one path for the current to take 123123123    VVVVIIIIRRRR VIR

11. 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

12. 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

13. Parallel Equivalent Circuits
 
1 2 3 23 2 3 1 23
123 1 2 3
123 1 23
1 2 3
1 2 3
1 2 3 1 2 3
1 1 1 1 1 1 1 1 1 1
1 1 1 1
1
1 1 1 1 1 1
 
        
 
       
 
      
   
let so
and
R R R R R R R R R R
R R I I I I
R R R R
I I I
V I R I I I
R R R R R R

14. 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.

15. 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.

16. 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.
22VPIRVIR 

17. 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:
VIRPVI  

18. 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
V
V I R I
R
V R
I I I
P V I
creases

19. 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:
   12111VIRPVIRRR

20. Bulbs in parallel experiment continued…
      1212111111 constant for the circuit, decreases increases increases as R decreasesThe bulbs do not change in btorightness, but the tal power of the circuit is increasedVVIRIRPVIRRRRRRVRIP

21. Light bulbs are not linear
• The resistance of light bulbs increases
with 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,
which is a very good conductor. It heats up easily.
      Tungsten 0.004403/ at 20 (i.e. 20 ) o C C T C

22. As light bulbs warm up, their resistance increases. If the current through them remains constant:
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.
2PIR

23. 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.

24. “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.

25. “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??
Temperature of bulbs increases
 resistance increases
 power dissipation (brightness) of bulbs
increases
2
2
2 2
Hot Cold
Hot Cold
Hot Cold
R R
P
P I R R
I
P P
I I
P P

   
 
 

26. 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
VIR

27. 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

28. The equipment you’ll be using:
- Voltmeter
- Breadboard
- Resistors
- 9V battery
Let’s do a quick review…

29. 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!

30. Voltmeter

31. Voltage:
Probes connect to either side of the resistor
Measuring Voltage

32. 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:

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

34. Parallel
Resistors are connected such that the current can take multiple paths

35. 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.

36. Thank you