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Ohm’s Law
EQUIPMENT NEEDED*
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Ammeter (0 to 0.5 A)
Voltmeter (0 to 10 V dc)
(or multi-meters)
Decade resistance box (0.1 to 99.9 Ω)
Rheostat ( ≈ 200 Ω )
Unknown resistance
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Battery or power supply
Switch
Connecting wires
*The ranges of the equipment are given as examples.
These may be varied to apply to available equipment.
THEORY
When a voltage or potential difference (V) is applied across a material, the current (I) in the
material is found to be proportional to the voltage, I α V. The resistance (R) of the material is
defined as the ratio of the applied voltage and the resulting current – that is,
R = V/I
(definition of electrical resistance)
(1)
For many materials, the resistance is constant, or at least approximately so, over a range
of voltages. A resistor that has constant resistance is said to obey Ohm’s law or to be “ohmic”.
From Eq. 1 , it can be seen that the unit of resistance is volt/ampere (V/A). However, the
combined unit is called the ohm (Ω), in honor of George Ohm. Note that to avoid confusion
with a zero, the ohm is abbreviated with a capital omega (Ω) instead of a capital “O”.
A plot of V versus I for an ohmic resistance is a straight line (Fig. 1). Materials that do
not obey Ohm’s law are said to be “nonohmic” and have a nonlinear voltage-current relationship.
Semiconductors and transistors are nonohmic.
Figure 1
Ohmic resistance.
A voltage-versus current graph for an ohmic
resistance is a straight line, the slope of which is equal to the value of the resistance (R = V/I).
In common practice, Ohm’s law is written
(2)
V = IR
where it is understood that R is independent of V. Keep in mind that Ohm’s law is not a
fundamental law such as Newton’s law of gravitation. It is a special case, there being no law that
materials must have constant resistance.
Consider the circuit diagram shown in Fig. 3. This is a series circuit. The applied
voltage is supplied by a power supply or battery Vt. Rh is a rheostat, a variable resistor that
allows the voltage across the resistance Rs to be varied. (This combination is sometimes called a
voltage divider because the rheostat divides the applied voltage across itself and Rs).
An ammeter A measures the current through the resistor Rs and a voltmeter V registers
the voltage drop across both Rs and the ammeter A. S is a switch for closing and opening
(activating and deactivating) the circuit.
Figure 2 Circuit diagram.
The voltmeter is connected in parallel across
the ammeter and the resistance Rh, is that of
the rheostat (continuously variable resistor).
Any component in a circuit that does not generate or supply a voltage acts as a resistance
in the circuit. This is true for the connecting wires, the ammeter, and the voltmeter. However,
the metallic connecting wires and the ammeter have negligibly small resistances, so they do not
greatly affect the current.
A voltmeter has a high resistance, so there is little current through the voltmeter. Hence,
to good approximations, the ammeter registers the current in the resistor, and the voltmeter reads
the voltage drop across the resistance. These approximations are adequate for most practical
applications.
Applying Ohm’s law to the portion of the circuit with Rs only, we have
Vs = IR s
( 3)
where V s and I are the voltmeter and ammeter readings, respectively. Notice that the same
current I flows through the rheostat Rh and the resistance Rs. The voltage drop across Rh is then
V h = IR h
( 4)
To apply Ohm’s law to the entire circuit , we use the fact that the applied voltage “rise” or the
terminal voltage V t of the voltage source must equal the voltage “drops” of the components
around the circuit. Then
V t=V
h
+Vs
or
V t = IR h + IR s = I(Rh + Rs)
( 5)
From Eq. 5, we see that for a constant R s, the current through this resistance, and hence
its voltage drop V can be varied by varying the rheostat resistance Rh. (The terminal voltage, V
is constant.) Similarly, when Rs is varied, the voltage Vs can be maintained constant by
adjusting Rh.
Experimental Procedure
1.
With the voltmeter, measure the terminal voltage of the power supply or battery, and
record it in Data Table 1. Start with the voltmeter connection to the largest scale, and
increase the sensitivity by changing to a smaller scale if necessary. Most common
laboratory voltmeters and ammeters have three scale connections and one binding post
common to all three scales.
It is good practice to take measurements initially with the meters connected to the largest
scales. This prevents the instruments from being “pegged” (the needle forced off scale
in galvanometer-type meters) and possibly damaged, should the magnitude of the voltage
or current exceed the smaller scale limits. A scale setting may be changed for greater
sensitivity by moving the connection (or turning the switch on a multimeter) to a lower
scale after the general magnitude and measurement are known.
Also, take care to ensure the proper polarity (+ and -); connect + to + and - to - .
wise, the meter will be “pegged” in the opposite direction.
Other
2.
Set up the circuit shown in the circuit diagram (Fig. 2) with the switch open. A standard
decade resistance box is used for Rs. Set the rheostat resistance Rh for maximum
resistance and the value of the Rs to about 50 Ω. Have the instructor check the circuit
before closing the switch.
A.
Variation of Current with Voltage
3.
After the instructor has checked the circuit, close the switch and read the voltage and
current on the meters. Open the switch after the readings are taken, and record them in
Data Table 1. Repeat this procedure for a series of four successively lower rheostat
settings along the length of the rheostat.
It is convenient for data analysis to adjust the rheostat (after closing the switch) so that
evenly spaced and convenient ammeter readings are obtained. The switch should be
closed only long enough to obtain the necessary readings. This prevents unnecessary
heating in the circuit and running the battery down.
4.
Repeat procedure 3 for another value of Rs (about 30 Ω).
5.
Repeat procedure 3 for the unknown resistance, and record data in Data Table 2.
Relatively low values of voltage may be required. Your instructor will discuss this and
the proper connection. Do not proceed with this procedure without instructions.
6.
Plot the results for both decade box resistances on a single Vs –versus-Is graph, and draw
straight lines that best fit the sets of data. Determine the slopes of the lines, and compare
them with the constant values of Rs of the decade box by computing the percent errors.
According to Ohm’s law, the corresponding values should be equal.
7.
Plot Vs versus I s for the unknown resistance. What conclusions about the unknown
resistance can you draw from the graphs?
B.
Variation of Current and Resistance (V s constant)
8.
This portion of the experiment uses the same circuit arrangement as before. In this case,
the voltage V s is maintained constant by adjusting the rheostat resistance Rh when the Rs
is varied.
Initially, set the rheostat near maximum resistance and the resistance Rs of the decade box
to about 100 Ω. Record the value of Rs in Data Table 3.
Close the circuit and adjust the rheostat for a convenient voltmeter reading (about 4 V).
Record the voltmeter reading as the constant voltage Vs in Data Table 3. Record the
current and resistance in the table. Open the circuit after making the readings.
9.
Repeat this procedure for four more successive steps of current by reducing the value of
Rs of the decade box. Keep the voltage across Rs constant for each setting by adjusting
the rheostat resistance Rh. Do not reduce Rs below 30 Ω.
10.
Plot the results on an Is-versus-1/Rs graph and draw a straight line that best fits the data.
(Reciprocal ohms, 1/R, is commonly given the unit name “mhos.”) Determine the slope
of the line, and compare it with the constant value of V s by computing the percent error.
According to Ohm’s law, these values, should be equal.
A.
Variation of Current with Voltage
Data Table 1
Terminal Voltage V t ___________
Constant Rs ___________________
Constant Rs _____________
Voltage Vs (
Voltage Vs (
Reading
)
Current Is ( )
)
Current Is ( )
1
2
3
4
5
Calculations
(show work)
Slope of lines
Don’t forget units
Percent error from Rs
__________________
_________________
__________________
_________________
Data Table 2
Unknown Resistance
Reading
1
2
3
4
5
6
7
Conclusions from graph:
Voltage Vs ( )
Current I s (
)
B.
Variation of Current with Resistance (V s constant)
Constant V s __________________
Data Table 3
Reading
Current Is
( )
Resistance Rs
( )
I/Rs
( )
1
2
3
4
5
Calculations
(show work)
Slope of line ___________________
Percent error from V s __________________________