A cylindrical conductor of length l and uniform area of cross-section A has resistance R. What is area of cross section of Another conductor of the same material of length 2l and resistance R ?
2A
twice
We know that the resistance of a conductor is given by the formula:
R = ρ * (l / A)
where ρ is the resistivity of the material, l is the length of the conductor, and A is the area of the cross-section.
Let's solve the equation for the area of the cross-section (A):
R = ρ * (l / A)
Divide both sides of the equation by ρ:
R / ρ = l / A
Now, if we have another conductor with length 2l and resistance R, we can substitute the given values into the equation:
R / ρ = 2l / A'
where A' is the area of the cross-section of the new conductor.
We can solve for A' by isolating it on one side of the equation:
A' = (2l * ρ) / R
Therefore, the area of the cross-section of the new conductor is (2l * ρ) / R.
To find the area of cross-section of another conductor with the same material but with a length of 2l and resistance R, we can make use of the formula for resistance of a conductor:
Resistance (R) = (ρ * L) / A
Where:
- R is the resistance of the conductor
- ρ (rho) is the resistivity of the material
- L is the length of the conductor
- A is the cross-sectional area of the conductor
Since the resistivity and the length of the conductor are constant (since they are made of the same material), we can set up the following equation:
R1 = (ρ * l) / A1 ----------> Equation 1 (For the given conductor)
R2 = (ρ * 2l) / A2 ----------> Equation 2 (For the other conductor)
Here, R1 is the given resistance (R) and l is the given length.
We can rearrange Equation 2 to solve for A2:
A2 = (ρ * 2l) / R2
Since we want to find the area of cross-section of the other conductor with resistance R, we can substitute R2 with R:
A2 = (ρ * 2l) / R
Therefore, the area of cross-section of the other conductor is given by (ρ * 2l) / R.