Experiment 20
Experiment 20: Ohm’s Law
Purpose
(1)To verify Ohm’s Law.
(2)To study resistors connected in series and in parallel.
Apparatus
(a) a DC Power Supply, a sample with 3 resistors; an ammeter
(b) a voltmeter; a supply of connectors
Theory
A) Ohm’s Law. When current I flows through a resistor,then the potential difference V (often simply called voltage) between its terminals is proportional to I as in
equation (1), where R is the resistance. / (1) / BASIC EQUATION
V = R · I
B) Combinations of Resistors. When two or more resistors ( R1, R2, R3,…) are connected in series (Fig. 1) then this combination is equivalent to a single resistor
of resistance Req given by (2).
/ (2) / BASIC FORMULAReq = R1 + R2 + R3+. . . . .
When two or more resistors are connected in parallel (Fig. 2) then the equivalent
resistance Req is given by (3).
/ (3) / BASIC FORMULA1 = 1 + 1 + 1 . . . .
Req R1 R2 R3
Procedure Part I: Ohm’s Law
a) Make sure that the DC power supply is off and unplugged. Make sure that the
regulating knobs are in minimum positions.
Your instructor will explain to you the operation of DC power supply, the ammeter, and the voltmeter.
b) Construct the circuit as in Fig. 3a, using the resistor marked R1in your sample. Use the 50 ma scale ammeter scale and make sure that + and – markings are exactly as in Fig. 3a.
c) Set the voltmeter scale to read 5 volt maximum. Attach connectors to your voltmeter
(suggestion: use a red connector for the + terminal and a black one for -). Connect the + terminal to point B (where the current enters the resistor) and the other one to point A.
Make sure all connections are tight. If you have a faulty connector, immediately hand it to your instructor (do not return it where you took it from!)
CALL YOUR INSTRUCTOR TO CHECK YOUR CIRCUIT. DO NOT PROCEED
WITHOUT HIS OR HER PERMISSION.
d) After your instructor’s approval, prepare on your data sheetyour first table, as shown. Plug in the power supply. With the
regulating knob(s) in Min position, turn the power “ON”.
Turn slowly the regulating knob(s) and watch both the ammeter and the voltmeter readings to increase (if not, turn off the power at once and call your instructor). Keep doing this until the ammeter reaches 50ma or the voltmeter reaches / RESISTOR R1
I
(ma) / V
(volts)
...... / ......
5 volts whichever comes first.
Record the current I and the voltage V to three significantdigits, by estimating fractions of smallest divisions on the scales.
e) Decreasing the current, record I and V four more times (a total of 5 readings), in
roughly equal intervals. The lowest current should be 5 to 10 ma.
f) Repeat the steps (d) and (e) for your resistors R2andR3, with maximum current
close to 50 ma but using the finest voltmeter scale possible for each given resistor
(it could be 2.5 volt scale).
Record the voltmeter scale used, for each sample.
g) Turn the power “OFF”, and record:
1) The uncertainties in your readings on all scales of ammeter and voltmeter
which you have used.
2) The zero readings of your ammeter: these are their readings when
they are completely disconnected from any circuits. They should be close to
zero, but not necessarily exactly so (consult your instructor, if in doubt).
Procedure Part II: Combinations of Resistors
h) Connect all three resistors R1 , R2 , R3 in series (if not sure how to do this, check with your instructor) and use the 10 volt scale on the voltmeter.
Record 5 runs as before. (Note: your maximum current may be less than 50 ma
because the voltage must not exceed 10mvolts).
j) Connect all these resistors in parallel (if not sure, call your instructor). Again, use the finestvoltmeter scale possible, with the maximum current close to 50 ma. Record
5 runs, as before.
k) Estimate (from your data in Part I) the values of R1 , R2 , R3 . Take the two higher resistances (record which ones you are using) and connect them in parallel.
Connect this combination in series with the remaining resistor (if in doubt, call
your instructor!). Record 5 runs, as usual.
BEFORE YOU LEAVE THE LAB:
A) Disconnect all wires, unplug the power supply, and clean up your station
.
B) Your data sheet should have 6 tables, clearly marked with: (i) which resistors were
used, (ii) which scales were used, (iii) the uncertainties of every scale used, (iv) zero
readings.
Lab Report
Part I
1) Using graph paper, plot V vs. I for each of your resistors R1 , R2 , R3 . Draw the line of best fit in each case and (from the slope) determine the resistance in ohms, to
3 significant digits.
Display all calculations on the graph sheet.
Part II.
2) Using graph paper, plot V vs. I for each of the three combinations. Determine Req for each case, as in (1) above.
3) From your results in (1) calculate the predicted (= theoretical) values of Req for each of the three combinations. Display the calculations clearly.
4) Summarize your resultsin the table shown. For
% discrepancies use the
predicted values as more
reliable (that is, refer to
them as if they were exact). / COMBINATION / PREDICTED R / MEASURED
R / %
DISCR.
ALL IN SERIES
ALL IN PARALLEL
SERIES & PARALLEL
5) Answer the Following:
Question #1: Explain, whether a line of best fit should, or should not, pass through the origin of the graph (V vs. I).
Question #2: Could the zero readings of your ammeter and voltmeter be also used
(as a data point) when drawing the graph? Explain.
Question # 3: Suppose somebody, using the same apparatus which you did use,
measures I = 45.5 ma, and V = 8.2 volts on some resistor.
On the basis of your recorded uncertainties for 50 ma and 10 volt
scales, what would be the maximum uncertainty ( in % ) in R if it
were calculated directly from formula (1)? (Physics 4 students should use calculus methods (estimating errors by differentials) to answer this question.
6) If your actual discrepancies in (3) are substantially different from your estimate in
Question #3, find and state the true causes of this.
1
If your voltmeter has no such scale, use the 3 volt scale but check with your Instructor
for a revision of the instructions for the experiment.