Ohm's Law
David Pan
Cluster 2
Cosmos
2015/07/27
Ⅰ. Abstract
The objective of several Ohm's experiments is trying to find the relationship between
three variables in the circuit. At first, Ohm does several experiments in order to find
what determine the resistance of circuit. After finding what determine the resistance of
circuit, Ohm varies three variables of circuit individually and finally establishes the
right law about the relationship between three variables in circuit. That is, the current
through a conductor between two points is directly proportional to the potential
difference across the two points and inversely proportional to the resistance of the
conductor.
Ⅱ. Introduction
In 1775, Henry Cavendish, of England, the first person who tries to find the relationship
between voltage, current and resistance, did a experiment about current and resistance.
He varies the length of a tube in order to vary the resistance and uses his body to sense
the strength of current because of his own body. He concludes that higher the resistance,
lower the current in the circuit.
In 1800, Volta invented one of the most important things in electrical study. That is the
voltaic piles. Voltaic piles provide relatively stable and constant current, which enable
scientists much more conveniently to study electricity.
In early eighteen century, Orsted discovered the phenomenon that wire which has
electricity passes through will form a magnetic field around it. This discovery enlighten
scientist and they make a new and rudimentary equipment which can measure the
strength of current. Later, scientists improved this equipment and it became a normal
equipment we always use to measure the current strength now-galvanometer. Using this
equipment, scientists can study the electricity more easily and humans are more close
to the reality of electricity.
In 1820, Sir Humphry Davy did a experiment about the relationship between the
resistance of a conductor, the length of the conductor and the cross-section of the
conductor. He concluded that wires having the same ratio of length to cross-section had
the same resistance, which accords to part Ⅱ of Ohm's law.
For centuries, these pioneers collected so many data about the relationship between
current, voltage and resistance but they still did not know and define some variables
and units. The investigation of Ohm perfectly solves these problems and establish a law
which we can use to predict the behavior of electricity.
Ⅲ. Material and Methods
Experiment 1
A. Material
1. voltaic piles
2. conductor which have different length
3. a resistor
4. torsion balance
B. Methods
In this experiment, Ohm connects voltaic piles, and a resistor with fixed
resistance in series. He first connects a shortest conductor to the circuit and
then he use torsion balance to measure the force of current. Then he replace
the shortest conductor with other longer conductor and use torsion balance to
measure the force of current. At last, compare force strength respectively to
conductors' length.
Experiment 2
A. Material
1. Voltaic pile
2. Galvanometer
3. Wires
4. Resistors with different material, cross-section and length
B. Methods
Ohm uses a voltaic pile which has fixed voltage. Then, he connects different
resistors with different material, cross-section and length and then he uses a
galvanometer to measure the current in the circuit with different resistor.
Experiment 3
A. Material
1. Voltaic pile
2. Galvanometer
3. Wires
4. 2 conductors with same cross-section and length but one is circular while
the other is flat.
B. Methods
Ohm uses a voltaic pile to provide same voltage on two conductors with
same cross-section and length but one is circular while the other is flat.
Meanwhile, he uses galvanometer to measure the current in the circuit
Experiment 4
A. Material
1. Thermocouple( a more stable electricity generator compared to voltaic pile)
2. Torsion Balance
3. Wires
4. conductors with different length
B. Method
In this experiment, Ohm uses thermocouple instead of voltaic piles.
Thermocouple is a more stable electricity source and we can change the voltage
through varying the temperature difference of the thermocouple. This
experiment is really similar to the first experiment. First, Ohm connects a
shortest conductor to the thermocouple and he uses torsion balance to measure
the force of current which can show the strength of current. Then he uses same
way to measure the current passes through other conductors with different
length. Then, he decreases the temperature difference between two ends of
thermocouple in order to decrease the voltage it provides. Then, he uses same
method to measure the current pass through different conductors again.
Ⅳ. Result
A. Experiment 1
In this experiment, the force of current decreases as the length of conductor
increases. Also the data Ohm recorded accords the graph v=0.41log(1+X).
B. Experiment 2
In this experiment, Ohm finds that the current passes through resistors which
have different materials but same length and cross-section is different.
However, he also finds that current passes through resistors which have same
material and same ratio of length to cross-section is same.
C. Experiment 3
In this experiment, Ohm finds that current pass through two conductors is same
when voltage on two resistors is same cross-section and length. Therefore, the
current is same because experiment 1 has proved that. Thus, we can conclude
that current is uniformly distributed throughout the section.
D. Experiment 4
In this experiment, the force of current decrease as the length of conductors
increases. After decreasing the temperature difference between two ends, which
means decreasing the potential difference between two ends, the force of
current still decreases as the length of conductors increases. However, the force
of current after decreasing the temperature is smaller than the force of current
before decreasing the temperature.
Ⅴ. Discussion
In the experiment 1,Because the force of current decrease, Ohm assumes that the
current also decreases. Thus, Ohm concludes that the current of circuit is inversely
proportional to the length of conductor. Also, analyzing his data, he implies that the
loss of potential difference can be formulated as v=m log(1+x/a), where a depends
on the length of conductor, m is the normal force and x is the resistance of
external resistor.
In the experiment 2, resistors which have different materials but same length and
cross-section have different current pass through while the voltage is same. It infers
that the resistance of these resistors is different. In addition, resistors which have
same material and same ratio of length to cross-section have same current pass
through while the voltage is same. It infers that these resistors have same
resistance. Experiment 1 indicates that the type of material is one of the variables
that determines the resistance of this material. Furthermore, the resistance of the
conductor is directly proportional to the ratio of length to cross-section.
In the experiment 3, although one resistor is circular and the other is flat, current
pass through two resistors is same when the voltage is same. The voltage on two
resistors is same and two resistors have same sum of area of cross-section.
Therefore, Ohm concludes that the current is uniformly distributed in the conductor
instead of what people believed before that the electricity on the surface of the
conductor.
In the experiment 4, the force of current decreases as the voltage deceases, which
means the current decreases as the voltage decreases. Also, the force of current
decreases as the length of conductors increases, which means that the current
decreases as the length of conductor increases. Thus, Ohm conclude that the current
of a circuit is directly proportional to the voltage of the circuit and is inversely
proportional to the length of conductor
Ⅵ. Conclusion
Through analyzing the data Ohm collects from the previous experiment, Ohm can
derive the formula to calculate the resistance of a resistance. In experiment 1 and 4,
Ohm has concluded that the resistance of a resistors is directly proportional to the length
of the resistor. In experiment 2, Ohm knows that the current uniformly distributed in
the resistor. In addition, experiment 1 proves that the resistance of the resistor is
proportional to the ratio of length of resistor to the cross-section of resistor, which
means the resistance of resistor is inversely proportional to the cross-section area.
What's more, in experiment 1 Ohm knows that type of material also will determine of
resistance of conductor.Thus, Ohm mixes these three finding into one formulaR=ρ(L/A).
In the experiment 4, Ohm also gradually understands that current is directly
proportional to the voltage of the circuit. After knowing that the resistance of resistor is
directly proportional to the length of resistor, Ohm can also conclude that current is
inversely proportional to the resistance of resistor since in experiment 4, current
decrease as the length of conductor increase, which means the resistance increases.
Ohm then mix these two conclusion into one formula-I=V/R.
The establishment of Ohm's law shows people a new understanding of electricity and
it indicates that people know more about electricity. People can use this law to control
electricity in some extent.
Ⅶ. References
John C. Shedd and Mayo D. Hershey. "The History of Ohm's Law". Popular Science.
Dec.1913. July 29. 2015 . Bonnier Corporation.
Keithley Joseph F. "The Story of Electrical and Magnetic Measurements: From 500 BC
to the 1940s". Institute of Electrical and Electronics Engineering. 1999. July 29. 2015.
Timbie H. William. "Elements of Electricity". Basic Electricity for Communication.
Fourth Edition. Massachusetts Institute of Technology. 1910. July 29. 2015
Robert A. Millikan and E. S. Bishop. "Elements of Electricity". American Technical
Society. 1917. July 29. 2015.
G. S. Ohm. "Die galvanische Kette, mathematisch bearbeitet". 1827. July 29. 2015.
Griffiths, David J. "Introduction to electrodynamics". Third Edition. Prentice Hall.
1999. July 29. 2015.
Ⅸ. Appendix
Graph about data of experiment 1
Graph show the accuracy of measurement in experiment 4