Answer:
R' = 4R
Hence, the resistance increases to four times its initial value as well.
Explanation:
The resistance of a conductor in terms of its physical dimensions can be given by the following formula:
[tex]R = \frac{\rho L}{A}\\[/tex] _______ equation (1)
where,
R = Resistance of the conductor
ρ = resistivity of the material of the conductor
L = Length of the conductor
A = Cross-sectional Area of the conductor
Now, if the length of the conductor is increased to four times, keeping other values constant, then:
[tex]R' = \frac{\rho L'}{A}\\\\R' = \frac{\rho (4L)}{A}\\\\R' = 4\frac{\rho L}{A}[/tex]
using equation (1):
R' = 4R
Hence, the resistance increases to four times its initial value as well.
