
Define 1 Ohm resistance. A student has a resistance wire of 1 Ohm. If the length of this wire is 50cm, to what length he should stretch it uniformly so as to obtain a wire of 4 Ohms resistance? Justify your answer.
Answer
149.4k+ views
Hint: From ohm’s law, the definition of 1 ohm resistance can be defined. The resistance of a substance is directly proportional to its length.
Formula used: In this solution we will be using the following formulae;
where is resistance, is voltage and is current.
where is the resistivity of the wire, is the length and is the cross sectional area.
Complete Step-by-Step Solution:
From the ohm law equation, the definition of 1 ohm, could be derived.
The ohm’s law equation is can be written as
where is resistance, is voltage and is current.
Hence, for 1 ohms, we can write
Hence, 1 ohm’s could be defined as the resistance to a 1 A current which causes 1 volt potential difference or voltage drop. Or it can be defined as the resistance value which would allow only 1 A of current to flow when the component is connected to a 1 volt source.
For the second part of the question, a student possesses a resistance wire of 1 ohms which has a length 50 cm. to what length should he stretch it uniformly to obtain a resistance wire of 4 ohms.
Recall that the resistance of a wire can be given as
where is the resistivity of the wire, is the length and is the cross sectional area.
Hence, if the all other properties are kept constant,
where is a constant.
Then,
Hence, by cross multiplication,
Hence, the length of the wire has to be stretched to 250 cm.
Note: In actuality, the wire would not need to stretch that far before the resistance actually attains 4 ohms as desired. This is due to the Poisson phenomenon, which is the fact that as the length stretches, the cross sectional area of the wire will reduce, hence creating a double effect of increment of resistivity (the smaller the cross sectional area, the lower the resistance).
Formula used: In this solution we will be using the following formulae;
Complete Step-by-Step Solution:
From the ohm law equation, the definition of 1 ohm, could be derived.
The ohm’s law equation is can be written as
Hence, for 1 ohms, we can write
Hence, 1 ohm’s could be defined as the resistance to a 1 A current which causes 1 volt potential difference or voltage drop. Or it can be defined as the resistance value which would allow only 1 A of current to flow when the component is connected to a 1 volt source.
For the second part of the question, a student possesses a resistance wire of 1 ohms which has a length 50 cm. to what length should he stretch it uniformly to obtain a resistance wire of 4 ohms.
Recall that the resistance of a wire can be given as
Hence, if the all other properties are kept constant,
Then,
Hence, by cross multiplication,
Hence, the length of the wire has to be stretched to 250 cm.
Note: In actuality, the wire would not need to stretch that far before the resistance actually attains 4 ohms as desired. This is due to the Poisson phenomenon, which is the fact that as the length stretches, the cross sectional area of the wire will reduce, hence creating a double effect of increment of resistivity (the smaller the cross sectional area, the lower the resistance).
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