Experiment II

Ohm's Law and Resistor Circuits

**Introduction**

In this experiment you will test Ohm's "law" for a carbon
resistor. Then, using this "law", you will determine the equivalent
resistance of 2 or more resistors connected in series and parallel.

**Theory**

Ohm's law states that for an ohmic conductor, the current I through
the conductor is directly proportional to the voltage V applied across
the conductor. That is,

I V or I = CV where C is a constant. (2.1)

The constant of proportionality C is written as 1/R so that

I = V/R and R is called the resistance. (2.2)

Thus, the higher the resistance the lower the current for a given applied
voltage. R has units of volts/amps or ohms (W).

Ohm's law, V = IR is only an approximation for the electrical behavior
of certain materials under certain conditions. The resistance of many conductors
such as metals increases with increasing temperature. When a current I
flows through a resistance R, heat is generated at the rate, I^{2}R
(Joule heating). Thus, if enough current flows through a resistor to cause
it to heat up appreciably, it will behave in a non-ohmic way and one cannot
speak of the resistor as having a certain fixed resistance for all currents.

**Procedure**

**Part I. A study of Ohm's Law**

Your instructor will discuss with you the use of ammeters and voltmeters.
The main points to remember are that a voltmeter has a high resistance
and is attached *across *the ends of a circuit element to measure
the voltage between the ends of the element. An ammeter has a low resistance
and is *never placed across* the ends of circuit element. It is always
wired into a circuit so that it *acts as a connecting wire* to the
circuit element whose current is to be measured.

Construct the circuit below to study Ohm's law for the resistor.

The element on the left is a power supply set at 5 VDC. The 340 W
rheostat is connected as a voltage divider. By moving the rheostat wiper,
the voltage across R can be varied from 0 to 5 V. Use one of the three
carbon resistors on the board given you as R.

Note that the voltmeter V is connected across the ends of R. V and R
are said to be connected in parallel. On the other hand, the ammeter A
connects the rheostat to the resistor and is said to be in series with
the resistor.

Measure the current I through R for at least 5 voltages across R between
1 and 5 volts. Note that if you change to a new ammeter scale after you
have set the voltage, you will need to reread or reset the voltage because
the ammeter resistance changes with a change in scale.

Make a linear plot of V versus I. You may do this on the computer using
the program "Quattro Pro". Assume that the meters are accurate
to a few percent in estimating your error in V. (We will ignore the fact
that the meter readings for small deflections tend to be less accurate
than those for large deflections.) Do your data support a straight line
fit? That is, does Ohm's law V = IR appear to be obeyed? What value do
you obtain for R?

Compare the value of R obtained from your analysis with the value given
by the color codes on the resistor. (See Figure 2.2.) Then
compare your value for R with the value obtained by a direct measurement
of R using an ohmmeter furnished by your instructor. Note on determining
the value of a resistor using its color bands; Black=0, Brown=1, Red=2,
Orange=3, Yellow=4, Green=5, Blue=6, Violet=7, Gray=8, and White=9; Silver=10%
and Gold=5%.

**Part II**

**A. The Equivalent Resistance of two or more Resistors connected in
Series.**

Wire the series circuit as shown in Figure 2.3 using two of the carbon
resistors furnished. Measure the current *along* ab, cd and ef. Next
measure the voltage *across* af (V_{T}), bc (V_{1})
and de (V_{2}).

Note that the dashed circles indicate the different places you will
need to put the ammeter and voltmeter to make the required measurements.
It is generally best to wire up your circuits first *without* any
meters and then to insert and *remove them* as needed.

Attach the voltmeter to measure V. Set the power supply so that V_{T}
= 5 V. Then measure the voltages V_{1} and V_{2}, across
each of the resistors. Does V_{T} = V_{1} + V_{2}
within experimental error?

Now measure the current entering R_{1} on the + side, the current
flowing between R_{1} and R_{2} and the current leaving
R_{2}. How do these currents compare? What can you say about the
current anywhere in a series circuit?

Since you have measured V_{T} and I_{T}, you can determine
the equivalent resistance, R_{eq} of your circuit from Ohm's law,
V_{T} = I_{T}R_{eq}?

Similarly from I_{T}, V_{1} and V_{2} you can
determine R_{1} and R_{2}. Compare the sum R_{l}
+ R_{2} to R_{eq} as determined above. Does it appear that
R_{l} and R_{2} in series have an equivalent resistance
R_{eq} = R_{1} + R_{2}?

Note that once you have found R_{eq} for two resistors in series,
the addition of a third series resistor R_{3} gives a total equivalent
resistance of R_{eq}(1,2) + R_{3} = (R_{1} + R_{2})
+ R_{3} = R_{1} + R_{2} + R_{3}. *Hence
the equivalent resistance of any number of resistors in series is the sum
of the individual resistances.*

**B. The Equivalent Resistance of two or more Resistors connected in
Parallel.**

Wire the two resistors that you used above into parallel circuit as
shown in Figure 2.4.

Note that in drawing a circuit it is always assumed that the connecting
wires have a negligible resistance compared to any resistors in the circuit.
This being the case here, both R_{1} and R_{2} have the
same voltage V_{T}, across them. By definition, two in parallel
have the same voltage across them. Insert the voltmeter to measure this
voltage V_{T}. Adjust the power supply so that V_{T} =
5 V. Now measure the total current I_{T} and then the individual
currents I_{1} and I_{2} through, R_{1} and R_{2}.
Does I_{T} = I_{1} + I_{2} within experimental
error?

The equivalent resistance of R_{1} and R_{2} is again
defined by V_{T} = I_{T}R_{eq}.

What value do you find for R_{eq}? What values do you find for
R_{1} and R_{2}? Compare your value for 1/R_{eq}
with the sum 1/R_{1} + 1/R_{2}. Are your measurements consistent
with the statement that for two resistors in parallel,

(2.3)

Note that if a third resistor R_{3} were to be added in parallel
to R_{eq} of R_{1} and R_{2} the new equivalent
resistance would be given by

(2.4)

But this is just

(2.5)

so that the extension to any number of resistors in parallel is now
evident.

**Conclusions**

Summarize what you have learned about the voltages, currents, and equivalent
resistances in series and parallel resistor circuits.

**Part III.**

If you have the time, connect a small light bulb in the circuit shown
below.

Vary the power supply from 1 to 5 V and record the current I flowing through the bulb. Check to see if the light bulb obeys Ohm's law.

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This page last updated on December 30, 1996.

© 1996 Dr. H. K. Ng.

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