. The maximum allowable resistance for an underwater cable is one hundredth of an ohm per metre. If the resistivity of cooper is 1.54 × 〖10〗^(-8) Ω m, find the least diameter of a copper cable that could be used
(show work)
To find the least diameter of a copper cable that could be used with a maximum allowable resistance, we can use the formula for resistance:
R = (ρ * L) / A
where:
R is the resistance,
ρ is the resistivity of copper,
L is the length of the cable, and
A is the cross-sectional area of the cable.
In this case, the maximum allowable resistance per meter is given as one hundredth of an ohm per meter, which can be written as 0.01 Ω/m.
We need to rearrange the formula to solve for the cross-sectional area (A), which is related to the diameter (d) of the cable:
A = (π * d^2) / 4
Substituting the values into the resistance formula:
0.01 = (1.54 × 10^(-8) * L) / [(π * d^2) / 4]
Now we can isolate the diameter (d) by rearranging the equation:
d^2 = (1.54 × 10^(-8) * L) / [(π * 0.01) / 4]
d^2 = (1.54 × 10^(-8) * L) / (π * 0.01/4)
d^2 = (1.54 × 10^(-8) * L) / (π * 0.0025)
d^2 = 1.54 × 10^(-8) * L / (π * 0.0025)
Finally, taking the square root of both sides to solve for the diameter (d):
d = √ [1.54 × 10^(-8) * L / (π * 0.0025)]
Now, substitute the given values and solve for the least diameter:
d = √ [1.54 × 10^(-8) * L / (π * 0.0025)]
Note: The length of the cable (L) is not given in the question, so you would need to provide that value in order to calculate the least diameter.