A given wire has a resistance of 17.5 ohms. If its length is 560 m, how much length must be cut-off from the wire in order to reduce its resistance to 10 ohms?
To calculate the length that must be cut-off from the wire, we can use the formula:
R = ρ * (L/A)
Where:
R is the resistance
ρ (rho) is the resistivity of the material
L is the length of the wire
A is the cross-sectional area of the wire
First, let's rearrange the formula to solve for the length:
L = (R * A) / ρ
Since we are trying to find the length that needs to be cut-off, we can rewrite the formula as:
L_cut = L_initial - L_final
where:
L_cut is the length to be cut off
L_initial is the initial length of the wire
L_final is the final length of the wire
Now, let's calculate the length to be cut-off:
L_final = (R_final * A) / ρ
Given:
R_final = 10 ohms
L_initial = 560 m
R_initial = 17.5 ohms
To find the cross-sectional area A, we need to know the resistivity (ρ) of the wire material. Assuming the resistivity is constant, we can rearrange the formula for A:
A = (R_initial * L_initial) / ρ
Now we can substitute the values into the formulas:
A = (17.5 ohms * 560 m) / ρ
L_final = (10 ohms * A) / ρ
Finally, we can substitute the value of A into the second formula:
L_final = (10 ohms * [(17.5 ohms * 560 m) / ρ]) / ρ
This will give us the final length of the wire. To find the length that needs to be cut off, you can subtract the final length from the initial length:
L_cut = L_initial - L_final
Substituting the values and performing the calculations will give you the answer.
To solve this problem, we need to use the formula for the resistance of a wire:
R = ρ(l / A)
where R is the resistance, ρ (rho) is the resistivity of the material, l is the length of the wire, and A is the cross-sectional area of the wire.
In this case, we are given the resistance (R = 17.5 ohms) and the length (l = 560 m), and we need to find the length that needs to be cut off to reduce the resistance to 10 ohms. We can assume that the resistivity ρ and the cross-sectional area A of the wire remain constant.
First, let's rearrange the formula to solve for the length:
l = (AR) / ρ
Next, substitute the given resistance and length into the equation:
l = (AR) / ρ = (A * 17.5) / ρ
We can simplify the equation by assuming that the resistivity ρ and cross-sectional area A remain constant:
l = constant * R
Now, we can calculate the length needed to reduce the resistance to 10 ohms:
l = (A * 10) / ρ
Finally, to find the length that must be cut off, we subtract the length needed to reduce the resistance from the original length:
length to be cut off = original length - length needed to reduce resistance
length to be cut off = 560 m - [(A * 10) / ρ]
Since we don't have the specific values for the resistivity ρ and cross-sectional area A, we cannot calculate the exact length that needs to be cut off. To determine the length, you would need to know the resistivity and the cross-sectional area of the wire.