If the length of a wire is doubled and its cross – section area decreased to half ,the resistivity of the wire becomes
a)the same
b)four time
c)half
d)one fourth
e)double
Wire resistance is proportional to
(Length)/(Area).
You figure it out. L becomes 2L.
A becomes A/2
2L/(A/2) = 4 L/A
Half
To determine how changing the length and cross-sectional area of a wire affects its resistivity, we need to understand the relationship between these variables.
Resistance (R) is directly proportional to the resistivity (ρ), length (L), and inversely proportional to the cross-sectional area (A). Mathematically, it can be represented as:
R = ρ * (L / A)
In this scenario, the length of the wire is doubled (2L), and the cross-sectional area is decreased to half (A / 2). Let's substitute these values into the formula:
R = ρ * (2L) / (A / 2)
= ρ * 2L * (2 / A)
= 4 * ρ * L / A
So, we can see that the resistivity is multiplied by 4. Therefore, the answer is (b) four times.