Voltage: Ohms Law And Kirchhoffs Rules


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Voltage: Ohm's Law and Kirchhoff's Rules


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.

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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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