Question

Resistance of wire is \[R\] and cross-section area is \[A\] now the area is changed to \[N\] times. What will be the new resistance?

Answer 1

Hint: Here, we have to use the formula for resistance and use the original formula for resistance and consider it as old resistance then for new resistance we have to use the same formula but different values as mentioned in the given conditions of the question.

Complete step by step answer:
Let us consider the definition of resistance as: Resistance of the material or a conductor is directly proportional to the length of the conductor and inversely proportional to the area of cross-section of the conductor. Mathematically,
\[R = \rho \dfrac{l}{A}\]
\[\rho \] is the proportionality constant and the resistivity of the conductor.

Thus, according to the given condition, the area of cross-section is changed to the \[N\] times of \[A\]. So, the formula for new resistance is given by:
\[R' = \rho \dfrac{l}{{NA}}\]
Where, \[R'\] is the new resistance, \[\rho \] is the resistivity of the conductor, \[l\] is the length of the conductor and \[A\] is the area of the conductor.

So, new resistance can be written as:
\[R' = \dfrac{1}{N}\left( {\rho \dfrac{l}{A}} \right)\]
\[ \Rightarrow R' = \dfrac{1}{N}R\]........…... (Since,\[R = \rho \dfrac{l}{A}\])
Thus the new resistance is given by:
\[\therefore R' = \dfrac{R}{N}\]

Hence, the new resistance is $\dfrac{R}{N}$.

Note:The resistance is discussed in the simple formula given above, we just have to consider the given conditions and apply them in the formula. Here, we observe that the new resistance is equal to the fraction of original resistance to that of the no. of times.