ABSTRACT
Ohm's Law and Kirchhoff's rules is fundamental for the understanding of dc ci
rcuit. This experiment proves and show how these rules can be applied to so simple dc circuits.
IN
TRODUCTION
In the theory of Ohm's Law, voltage is simply proportional to current as il
lustrated in the proportionality, V=RI. As shown in this relation, V represent voltage which is the
potential difference across the two ends of a electrical conductor and between which an electric cu
rrent, I, will flow. The constant, R, is called the conductor's resistance. Thus by the Ohm's Law,
one can determine the resistance R in a DC circuit without measuring it directly provided that the
remaining variable V and I is known.
A resistor is a piece of electric conductor which
obeys Ohm's Law and has been designed to have a specific value for its resistance. As an extension
of the Ohm's Law, two more relationship can be drawn for electric circuits containing resistors co
nnected in series or/and parallel. For resistors connected in series, the sum of their resistance i
s, RTOTAL=R1+R2+ ..... +Rn . And for resistors connected in parallel, 1/RTOTAL==1/R1+1/R2+ ..... +1
/Rn . Complex dc circuit involving a combination of parallel and series resistors can be analyzed t
o find the current and voltage at each point of the circuit using 2 basic rules formulated by Kirchh
off. 1) The algebraic sum of current at any branch point in a circuit is zero. 2) The algebraic su
m of potential difference, V, around any closed loop in a circuit is zero. These rules and equation
s provided by the Ohm's law and the Kirchhoff rule can be experimentally tested with the apparatus a
vailable in the lab
EXPERIMENTAL METHOD
The apparatus used in the experiment includes
a Voltmeter, an Ammeter, some connecting wires and a series of resistors and light bulb with varies
resistance. This experiment could be divided into 5 sections which value of voltage and current me
asured is noted in all sections for further calculation. In the first section, in order to evaluat
e the reliability of Ohm's law, a dc circuit was constructed as FIG 2 (on p.4 ) using a resistor wit
h an expected resistance at 2400W*120W. In the second section, we were instructed to determine the
internal resistance of the voltmeter. Two dc circuit were constructed as FIG 1. and FIG 2. using a
resistor with an expected resistance at 820000W*41000W. In the third section, we were asked to jud
ge if the filament of a light bulb obey Ohm's law, this was done by constructing a dc circuit as FIG
1. with a light bulb instead of a resistor. Where in the forth section of the experiment, we explo
red the ability of multimeter to measure resistance directly and observed the difference in total re
sistance when two resistor at 270W*14W and 690W*35W were connected parallel or series together. And
finally, in the last section of this experiment, we were instructed to construct a circuit like th
e one shown in FIG 3. and test the Kirchhoff's rules where R1, R2, R3 are 270W*14W, 690W*35W and 240
0W*120W respectively. The voltage and current across and through each resistor was measured.
RESUL
TS AND DISCUSSION
Results from section 1 as we saw on Graph 1, the calculated resistan
ce was constant at 2448W*147W and this was within the experimental error of the actual resistance of
the resistor and so proved the accuracy of Ohm's law. Graph 2 and 3 summarized the differences in
total resistance led to the finding of the voltmeter's internal resistance in section 2. Since the
calculated total resistance , R1total , from circuit constructed as FIG 1. was, Resistor ,the resist
ance of the resistor alone, on the other hand, the calculated total resistance, R2total , from circu
it constructed as FIG 2. was , 1/Rresistor+1/ Internal resistance , a combination of resistance of
resistor and internal resistance of the voltmeter. Though a series of mathematical calculation, Int
ernal resistance can be solved. Our calculated Internal resistance is 18.21MW*0.02MW which was much
greater than the expected value of 10MW. This error is most likely due to 1) the inaccurate value
of given internal resistance since it's unlikely that all voltmeter have the same internal resistanc
e. 2) Unstability of power supply causes reading error. Graph 4 shown that growing light bulb did
not obey Ohm's law. Its resistance increased as it became brighter. The fact that resistance of a
metal increases with temperature is largely due to the heat, or kinetic vibration built up in metal
interferes with flow of electrons. In the fourth section of the experiment, the resistance measured
in parallel and series is 191W*1W and 950W*5W, very similar to the calculated resistance which is 1
94W*13W and 960W*37W respectively. And in our last section, to verify Kirchhoff's rules, I2+I3=3.7
0mA*0.04mA is approximately equal to I1 which is 3.79mA*0.03mA. Also, Vbattery+V1+V2= Battery +V1+V
3 where both are equal to 0V.
CONCLUSION
This experiment show that most dc circuit p
roblems can be solve by Ohm's law and Kirchhoff's rules which interested in voltage current and resi
stance.
REFERENCES M.M.Sternheim, J.W.Kane. General Physics 2nd edition John Wiley " Sons, Inc. 19
91. Canada. p.434-435
F.Hynds. First Year Physics Laboratory Manual 1995-1996 University of Toront
o
Bookstores. 1995. Toronto, Canada. p.74-76abstract kirchhoff rules fundamental understanding circ
uit this experiment proves show these rules applied simple circuits introduction theory voltage simp
ly proportional current illustrated proportionality shown this relation represent voltage which pote
ntial difference across ends electrical conductor between which electric current will flow constant
called conductor resistance thus determine resistance circuit without measuring directly provided th
at remaining variable known resistor piece electric conductor which obeys been designed have specifi
c value resistance extension more relationship drawn electric circuits containing resistors connecte
d series parallel resistors connected series their rtotal resistors connected parallel rtotal comple
x circuit involving combination parallel series analyzed find current voltage each point using basic
rules formulated kirchhoff algebraic branch point zero algebraic potential difference around closed
loop zero these equations provided kirchhoff rule experimentally tested with apparatus available ex
perimental method apparatus used experiment includes voltmeter ammeter some connecting wires light b
ulb with varies this experiment could divided into sections value measured noted sections further ca
lculation first section order evaluate reliability constructed using resistor with expected second s
ection were instructed determine internal voltmeter were constructed using resistor expected third s
ection were asked judge filament light bulb obey done constructing light bulb instead where forth ex
plored ability multimeter measure directly observed difference total when together finally last inst
ructed construct like shown test where respectively across through each measured results discussion
results from graph calculated constant within experimental error actual proved accuracy graph summar
ized differences total finding voltmeter internal since calculated total from constructed alone othe
r hand calculated from rresistor internal combination though mathematical calculation solved much gr
eater than expected value error most likely inaccurate given since unlikely that have same unstabili
ty power supply causes reading error graph shown that growing obey increased became brighter fact me
tal increases temperature largely heat kinetic vibration built metal interferes flow electrons fourt
h measured very similar respectively last verify approximately equal also vbattery battery where bot
h equal conclusion show most problems solve interested references sternheim kane general physics edi
tion john wiley sons canada hynds first year physics laboratory manual university toronto bookstores
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