Question
Question: Define 1 Ohm resistance. A student has a resistance wire of 1 Ohm. If the length of this wire is 50c...
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.
Solution
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;
R=IV where R is resistance, V is voltage and I is current.
R=ρAl where ρ is the resistivity of the wire, l is the length and A 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
R=IV where R is resistance, V is voltage and I is current.
Hence, for 1 ohms, we can write
1Ω=1A1V
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
R=ρAl where ρ is the resistivity of the wire, l is the length and A is the cross sectional area.
Hence, if the all other properties are kept constant,
lR=k where k is a constant.
Then,
l1R1=l2R2
⇒501=l24
Hence, by cross multiplication,
l2=50×4=250cm
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).