ABSTRACT
Ohm's Law and Kirchhoff's rules is fundamental for the understanding of dc circuit.
This experiment proves and show how these rules can be applied to so simple dc circuits.
INTRODUCTION
In the theory of Ohm's Law, voltage is simply proportional to current as illustrated 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 current, 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 connected in series
or/and parallel. For resistors connected in series, the sum of their resistance is,
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 to find the current and voltage at each point of the circuit
using 2 basic rules formulated by Kirchhoff. 1) The algebraic sum of current at any
branch point in a circuit is zero. 2) The algebraic sum of potential difference, V,
around any closed loop in a circuit is zero. These rules and equations provided by the
Ohm's law and the Kirchhoff rule can be experimentally tested with the apparatus
available 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 measured is noted in
all sections for further calculation. In the first section, in order to evaluate the
reliability of Ohm's law, a dc circuit was constructed as FIG 2 (on p.4 ) using a
resistor with 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 judge 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 explored
the ability of multimeter to measure resistance directly and observed the difference in
total resistance 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 the one shown in FIG 3. and test the Kirchhoff's
rules where R1, R2, R3 are 270W*14W, 690W*35W and 2400W*120W respectively. The voltage
and current across and through each resistor was measured.
RESULTS AND DISCUSSION
Results from section 1 as we saw on Graph 1, the calculated resistance 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 resistance of the resistor alone, on the other hand, the
calculated total resistance, R2total , from circuit 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,
Internal 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 resistance. 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 194W*13W and 960W*37W respectively. And in our last
section, to verify Kirchhoff's rules, I2+I3=3.70mA*0.04mA is approximately equal to I1
which is 3.79mA*0.03mA. Also, Vbattery+V1+V2= Battery +V1+V3 where both are equal to
0V.
CONCLUSION
This experiment show that most dc circuit problems can be solve by Ohm's law and
Kirchhoff's rules which interested in voltage current and resistance.
REFERENCES
M.M.Sternheim, J.W.Kane. General Physics 2nd edition John Wiley & Sons, Inc. 1991.
Canada. p.434-435
F.Hynds. First Year Physics Laboratory Manual 1995-1996 University of Toronto
Bookstores. 1995. Toronto, Canada. p.74-76
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