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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