Ohms Law

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Ohms Law

• Mitsuko J. Osugi
• Physics 409D
• Winter 2004
• UBC Physics Outreach

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Ohms 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 Voltage (Volts V) I Current (Amperes
A) R Resistance (Ohms O)
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Current and Voltage Defined
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. If there is no voltage,
electrons dont move, therefore there is no
current. Difference in electrical charge
between two points creates difference in
potential energy, which causes electrons to flow
from an area with lots of electrons (negative
terminal) to an area with few electrons (positive
terminal), producing an electric current.

• Electric Current flow of electrons from the
  negative terminal to the positive one
• Conventional Current
• (the current in electrical circuits)
• Flow of current from positive terminal to the
  negative terminal.
• Current has units of Amperes (A) is measured
  using ammeters.
• Voltage
• Energy required to move a charge from one point
  to another.

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Linearity of Voltage and Current for Resistors
which Obey Ohms Law
Voltage and current are linear when resistance is
held constant.
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Ohmic Resistors

• Metals obey Ohms Law 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.

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Ohms Law continued
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Ohms 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
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Kirchhoffs Current Law

• Current into junction Current leaving junction

The amount of current that enters a junction is
equivalent to the current that leaves the junction
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Kirchhoffs Voltage Law

• Net Voltage for a circuit 0

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

• Current is constant
• Why?
• Only one path for the current to take
• Kirchhoffs Current Law
• Voltages through circuit equals zero
• Kirchhoffs Voltage Law

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Series Equivalent Circuit
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Experiment 1

• One 10O resistor connected to the 6V power source
  (batteries). Add another 10O resistor to the
  circuit in series to the first resistor.
• Q What is the equivalent resistance, R? What
  will happen to the value of the current through
  each resistor? What will happen to the value of
  the voltage across each resistor?

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Experiment 1 What is happening in theory
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Experiment 1The actual 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.

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Parallel Circuit

• Voltage is constant
• Why?
• There are 3 closed loops in the circuit, which
  means the voltage though each loop is equivalent
  to the voltage supplied (like in a series
  circuit)
• Branch currents add to equal total current

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Parallel Equivalent Circuits
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Experiment 2

• One 10 ohm resistor connected to the battery.
  Connect a second 10O resistor in parallel to the
  first one
• Q What will the new resistance be? What will
  happen to the current through each resistor and
  the voltage across each component of the circuit?

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Experiment 2What is happening in theory
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Experiment 2The actual data
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• Weve now looked at how basic electrical circuits
  work with resistors that obey Ohms Law linearly.
  
• We understand quantitatively how these resistors
  work, but lets see qualitatively using light
  bulbs.
• Let us also determine if light bulbs also obey
  Ohms Law linearly.

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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.

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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.

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Experiment 3

• One bulb connected to the 6V power source. Add
  another bulb to the circuit in series.
• Q What is the initial current through the
  circuit? When the second bulb is added, will the
  bulbs become brighter, dimmer, or not change?
• We can use Ohms Law to approximate what will
  happen in the circuit

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Experiment 3The qualitative results (with some
theory)
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Experiment 3Some numbers

• Lets see what kind of values we find for the
  voltage across the light bulbs, and the current
  through the bulbs.

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Experiment 4

• Have one bulb connected to the 6V power source.
  Add a second bulb to the circuit in parallel.
• Q What is the initial current through the
  circuit? What happens when the second bulb is
  added?
• ? We can use Ohms Law to approximate what will
  happen in the circuit

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Experiment 4The qualitative results(with some
theory)
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Experiment 3Some numbers

• Lets see what kind of values we find for the
  voltage across the light bulbs, and the current
  through the bulbs.

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Light bulbs do not obey Ohms Law

• Bulbs are non-linear conductors
• (R increases with temperature)

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The filaments of light bulbs are made of
Tungsten, which is a very good conductor. It
heats up easily.
As light bulbs warm up, their resistance
increases. If the current through them remains
constant
They glow slightly dimmer when first plugged
in. Why? R increases but I remains constant ? P
increases Most ohmic resistors will behave
non-linearly outside of a given range of
temperature, pressure, etc.
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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.
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Memory Bulbs Experiment

• Touch each bulb in succession with the wire,
  completing the series circuit each time
• Q What is going to happen?
• Pay close attention to what happens to each of
  the bulbs as I close each circuit.

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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

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Conclusion

• Ohmic resistors obey Ohms Law
• Resistance is affected by temperature. The
  resistance of a conductor increases as its
  temperature increases.
• Light bulbs do not obey Ohms Law
• Tungsten is such a good conductor that their
  resistance depends on their temperature
• As their temperature increases, the power
  dissipated by the bulb increases
• i.e. They are brighter when they are hotter