Question

12 ohm resistance wire is doubled on itself calculate the new resistance of the wire

Answer 1

Resistance=ρL/A
Here, Resistance=12ohm
Therefore, 12=ρL/A
In second case, Resistance,R'=ρL'/A'
As the wire is doubled so L'=L/2, A'=2A
So new resistance,R'=ρL/4A=(1/4)ρL/A
But ρL/A=12
So, R'=12/4=3Ω

Answer 2

Answer:

R' = 3 ohms

Explanation:

The resistance of the wire is 12 ohms. We know that the resistance of object is given by :

$R=\rho \dfrac{l}{A}$

$12=\rho \dfrac{l}{A}$

l and A is the length and the area of cross section.

If the length of wire is doubled it means its length will get half and area of cross section will get doubled. New length, l' = l/2 and A' = 2A

$R'=\rho \dfrac{l/2}{2A}$

$R'=\dfrac{1}{4}\rho \dfrac{l}{2}$

$R'=\dfrac{1}{4}\times 12$

$R'=3\ \Omega$

So, the new resistance of the wire is 3 ohms. Hence, this is the required solution.