Download Lab4_EmfandTerminalVoltage

Phy132/222 Experiment
Emf and Terminal Voltage
(revised 6/17/08T)
Name: _______________________________
Date: _____________
Lab Partners: ________________________________________
Introduction: If you separate positive charges from negative charges an electric field will exist between
the net charge distributions. Any charge present in this electric field will be set in motion. As you learned in
class, a charge moving due to an electric field is moving through a potential difference. Just as a glass will
always fall to the floor and never up onto a table, and water always flows down hill, from a higher to a lower
gravitational potential energy; positive charges always flow from a high electric potential to a low electric
potential. In practice how do you separate charges to produce an electric field and create the resulting
potential difference? A battery is one such device that maintains a steady voltage. This potential difference is
not maintained indefinitely. Everyone has replaced a battery that has run down. Your cell phones indicate
how long the battery will last before it will need to be recharged. Batteries set up a potential difference
resulting in an electric field in the wires of the circuit through a complex chemical reaction. As you may
recall from chemistry class, no chemical reaction goes on indefinitely. There is a limited amount of reactants
contained inside your battery, and as those reactants start to run low the battery is no longer able to maintain
the indicated voltage. An old battery may be labeled 9.0 V, but a voltmeter will show that it can only
maintain a voltage of 8.6 V.
To model the slowing down of the reaction rate of a battery over time we say the battery has an internal
resistance. As the battery ages the decrease in the reaction rate is indicated by an increase in the internal
resistance. Consider the diagram below.
V
+
-
r
Emf
Figure 1
The Emf, ε is the potential difference across the terminals of the battery when no current is flowing in a
circuit. This is the potential difference we expect from the battery. The terminal voltage, Vt is the potential
difference across the terminals of the battery when a current is flowing in the circuit. If you have a new
battery the Emf and Vt will be indistinguishable. Over time, as the battery wears out, the Vt will be less than
the Emf. We can use conservation of energy and the diagram above to write a relationship between the
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terminal voltage, Emf, and the internal resistance. The Emf is the energy the battery can potentially provide
to the circuit. The internal resistance takes away from that, just as a resistor in a circuit would (Vr = Ir). What
is left over is the terminal voltage.
Vt = ε
– Ir
Part I: Set Up
The goal of this lab is to measure the internal resistance of a battery. First set up the circuit shown in the
diagram below
A
V
Emf
Rh
Figure 2
The symbol Rh represents a rheostat. A rheostat is a variable resistor. As you slide the tap on top of the
rheostat from one side to the next you vary the amount of the coil that the current has to pass through. If you
recall from class that R α L, you will recognize that as the amount of coil that the current has to pass through
increases, the resistance of the rheostat increases. You instructor will demonstrate this in class, and indicate
which side of the rheostat the tap needs to be placed on to give you the maximum resistance.
Part II: Procedure
Start with the rheostat set at its maximum resistance. Close the switch and measure the voltage across the
battery and the current in the circuit, then open the switch. Repeat seven more times by setting the rheostat to
seven successively smaller resistances. Make sure that you have moved the tap far enough so that you do not
measure the same voltage and current twice. Be sure that you do not keep the circuit closed very long. Why
is this a good idea? Plot the Voltage of the battery versus the Current in the circuit using Logger Pro. Which
Curve Fit Function should you apply to your data? Use the equation from the curve fit to determine the
internal resistance of your battery.
After you have finished with the first battery get a second battery with a different Emf and repeat. When you
are finished, proceed to the Questions section.
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Data
Emf 1
Rheostat Step
Voltage V
(
)
Current I
( )
1
2
3
4
5
6
7
8
Slope
y-intercept
x-intercept
Calculations (show work below)
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Emf 2
Rheostat Step
Voltage V
(
)
Current I
( )
1
2
3
4
5
6
7
8
Slope
y-intercept
x-intercept
Calculations (show work below)
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Questions
1.
Which Curve Fit function did you use to fit your data?
What does the slope of the graph represent?
2.
What do the y- intercept and the x-intercept of your graphs represent physically?
3.
Is it possible to determine the resistance of the rheostat using the data from this lab? If so, calculate it
and show your work below. If not, explain why it is not possible.
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