The resistance of a 395 m long aluminum rod is 3580 .
A. Find the cross-sectional area of the rod
mm2
B. Find the current in the rod when a potential difference of 14 V is applied across the ends.
A
To find the cross-sectional area of the rod, we can use Ohm's Law, which states that the resistance (R) of a conductor is equal to the resistivity (ρ) times its length (L) divided by its cross-sectional area (A). Mathematically, this can be written as:
R = ρ * L / A
Rearranging the equation, we can solve for the cross-sectional area (A):
A = ρ * L / R
Given that the length of the aluminum rod (L) is 395 m and the resistance (R) is 3580 Ω, we also need to know the resistivity (ρ) of aluminum. The resistivity of aluminum is approximately 0.0282 Ω mm^2/m.
Plugging in the values into the equation, we can find the cross-sectional area (A):
A = (0.0282 Ω mm^2/m) * (395 m) / (3580 Ω)
A = 0.031 mm^2
Therefore, the cross-sectional area of the aluminum rod is 0.031 mm^2.
To find the current in the rod when a potential difference of 14 V is applied across the ends, we can use Ohm's Law again. Ohm's Law states that the current (I) flowing through a conductor is equal to the potential difference (V) across the conductor divided by its resistance (R). Mathematically, this can be written as:
I = V / R
Given that the potential difference (V) is 14 V and the resistance (R) is 3580 Ω, we can calculate the current (I):
I = 14 V / 3580 Ω
I ≈ 0.00391 A
Therefore, the current in the rod when a potential difference of 14 V is applied across the ends is approximately 0.00391 A.