Ohms Law
Theory
The definition of resistance
R=
V
I
can also be viewed as a relationship between the voltage V across and the current I through a conductor.
This is known as Ohm’s law, and is expressed in the form
V = IR.
(1)
If this voltage-current relationship is linear then the conductor is said to be ohmic; conductors in which these
quantities are not proportional would therefore be characterized as non-ohmic. In this experiment, you will
identify circuit elements as being either ohmic or non-ohmic by analyzing voltage-current data graphically.
Apparatus
Power supply, DMMs, Decade resistance, Resistor, Bulb, Diode, Wires.
Procedure
The experimental circuit is shown below.
V
VS
r
r
+
−
Power Supply
r AAA
RL
r AAA
RE
V
VL
A variable voltage source (the power supply) is connected across the conductor being tested RE and a decade
resistance RL connected in series. This added resistance not only limits the current through the conductor
but also provides a more stable circuit.
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Although Ohm’s law applies to the voltage and current associated with a conductor, in this experiment we
will measure voltage only – and not even across the conductor we are testing. However, if we know the source
voltage VS and the voltage across the decade resistance VL , then we can calculate not only the voltage VE
across the conductor in question, but the current IE through it as well.
Since the resistances RE and RL are in series, the voltage VE across the conductor is given by
V E = VS − V L .
(2)
The current IE through the conductor is given by
IE =
VL
.
RL
(3)
Resistor
1. Assemble the circuit above with the resistor as RE . Set the decade resistance to 200Ω; this is RL .
2. Turn on the power supply and adjust VS from 0V to 10V in (roughly) 1V increments. At each step,
record the voltages VS and VL . When done, return the power supply to 0V and turn it off.
3. Switch the leads at the power supply and repeat Step 2. Since the current direction here is opposite
of before, record all values as shown; i.e., negative.
Bulb
1. Reset RL to 25Ω and repeat the procedure with the bulb as RE .
Diode
1. Reset RL to 500Ω and assemble the circuit with the diode as RE (the cathode should be connected to
the negative side of the power supply).
2. Repeat the procedure, varying VS from 0V to 2V in (roughly) 0.2V increments (start the voltmeter
measuring VL on the 200m scale and switch to a higher scale when necessary).
3. After switching the leads at the power supply, vary VS from 0 to 10V in (roughly) 1V increments
(again, start with the 200m scale for VL ).
Analysis
Resistor
1. Plot the current IE as a function of the voltage VE over the entire range of VE .
2. Fit your data to the appropriate function and state the full equation relating current and voltage for
the resistor.
3. Is the resistor an ohmic device?
4. Use the coefficient(s) in the regression equation returned to determine the resistance of the resistor.
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Bulb
1. Plot the current IE as a function of the voltage VE over the entire range of VE .
2. Is the bulb ohmic?
3. Calculate the base-10 logarithm of IE and VE (positive values) and plot a second graph of log IE vs.
log VE .
4. What type of function fits the data here? Fit this function to your data and use the coefficient(s)
returned to write the implied power function relating current and voltage for the bulb. Use the fact
that any power function
Y = CX n
can be made linear by taking the logarithm of both sides.
5. Does the resistance offered by the bulb increase or decrease with increasing voltage? How do you know
this?
Diode
1. Plot the current IE as a function of the voltage VE over the entire range of VE .
2. Is the diode ohmic?
3. Calculate the base-e (natural) logarithm of IE (positive values) and plot a second graph of ln IE vs.
VE .
4. What type of function fits the data here? Fit this function to your data and use the coefficient(s)
returned to write the implied exponential function relating current and voltage for the diode. Use the
fact that any exponential function
Y = CeDx
can be made linear by taking the natural logarithm of both sides.
5. Go back to the original graph of IE vs. VE for the diode; if you were to extend what appears to be the
linear portion of the curve (positive side) downward, where would it cross the x-axis? Adding another
trendline for the data here will be helpful. What do you think is the significance of this value?
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