A cylindrical conductor of length l and unifrom area of across section A has resistance R another conductor of length 2l and resistance R of the same material has area of across section
To find the area of the cross-section of the second conductor, we need to use the formula for resistance:
R = (ρ * l) / A,
where R is the resistance, ρ is the resistivity of the material, l is the length of the conductor, and A is the cross-sectional area.
Since both conductors are made of the same material, their resistivities are the same. Let's say the resistivity of the material is ρ.
For the first conductor:
Resisitance (R1) = R
Length (l1) = l
Area (A1) = A
For the second conductor:
Resistance (R2) = R
Length (l2) = 2l
Area (A2) = ?
We can rearrange the equation to solve for the cross-sectional area (A):
A = (ρ * l) / R
For the first conductor:
A1 = (ρ * l1) / R1 = (ρ * l) / R
For the second conductor:
A2 = (ρ * l2) / R2 = (ρ * 2l) / R
So, the cross-sectional area of the second conductor (A2) is twice the cross-sectional area of the first conductor (A1).
Therefore, A2 = 2 * A1 = 2 * A.
To find the area of the cross-section of the second conductor, we can use the given information about the first conductor. Let's break down the problem step by step:
1. In the first conductor, we are given that the length is "l" and the area of the cross-section is "A". The resistance is given as "R". We can use the formula for resistance of a conductor:
Resistance (R1) = resistivity (ρ) * (Length (l1) / Area (A1))
2. We also know that the second conductor has a length of "2l" and a resistance of "R", but the area of the cross-section is unknown (let's call it A2). Using the same formula, we substitute the given values:
R = ρ * (2l) / A2
3. Now, we can equate the two resistances (R1 and R2) since they are made from the same material:
R1 = R2
Therefore, we can set up the equation:
ρ * l / A1 = ρ * (2l) / A2
4. We can simplify the equation by canceling out the ρ and l terms:
1 / A1 = 1 / A2
5. Finally, we can solve for A2 by taking the reciprocal of both sides of the equation:
A2 = A1
Hence, the area of the cross-section of the second conductor (A2) is equal to the area of the cross-section of the first conductor (A1).