The resistance of 10m long wire is 10 . Its length is increased uniformly by 25% by stretching the wire
uniformly. The resistance of wire will change to (approximately)
(A) 12.5 (B) 14.5 (C) 15.6 (D) 16.6
the mass, density and volume are assumed not to change
R is old radius
Rn is new radius
V = pi R^2 L
Vn = pi Rn^2 (1.25) L
so
1.25 Rn^2 = R^2
resistance = k *Length/area
new area = old are /1.25
new length = old length*1.25
so
new redistance = old resistance *1.25/(1/1.25)
or
1.5625 * old
so C
To solve this problem, we need to understand the relationship between resistance, length, and cross-sectional area of a wire.
Resistance (R) is directly proportional to the length (L) of a wire and inversely proportional to the cross-sectional area (A) of the wire. This relationship can be defined by Ohm's Law:
R = ρ * (L / A)
Where:
R is the resistance
ρ (rho) is the resistivity of the material (a constant that depends on the material)
L is the length of the wire
A is the cross-sectional area of the wire
In this case, we are given that the resistance of a wire is 10Ω and its length is increased uniformly by 25% (which means the new length will be 125% of the original length). Let's assume the original length was L1, so the new length (L2) can be calculated as:
L2 = 1.25 * L1
To find the new resistance (R2), we need to substitute the values into the equation:
R2 = ρ * (L2 / A2)
Now, we need to determine the relationship between the original and new cross-sectional areas. Since the wire is stretched uniformly, the cross-sectional area will change in the same proportion as the length. In other words:
A2 = 1.25 * A1
Substituting this into the equation for R2:
R2 = ρ * (L2 / (1.25 * A1))
Now we can substitute the given values into the equation. Since we are not given any other information about the material or the cross-sectional area, we can cancel out ρ and calculate the resistance ratio:
R2/R1 = (L2 / (1.25 * A1)) / (L1 / A1)
= (L2 / L1) / 1.25
= (1.25 * L1 / L1) / 1.25
= 1
This means that the resistance does not change when the wire is stretched uniformly without any change in the material or cross-sectional area. Therefore, the resistance of the wire will remain 10Ω.
So, the answer is not given in the options.