Final answer:
The resistance of the wire is 0.1 ohm. The resistance of one meter of the wire is 0.01 ohm. The currents in each wire are 0.5772A and 0.23088A.
Step-by-step explanation:
In order to find the resistance of a wire, we can use the formula R = (p * L) / A, where R is the resistance, p is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire.
Given that the wire is 10m in length, has a resistivity of 3.14x10-8 ohm, and a radius of 1mm, we need to calculate the cross-sectional area of the wire first. The formula for the area of a circle is A = πr2 , so the area of the wire is A = π(0.001m)2 = 3.14x10-6 m2.
Now we can substitute the values into the resistance formula: R = (3.14x10-8 ohm.m)(10m) / (3.14x10-6 m2) = 0.1 ohm.
To find the resistance of one meter of the wire, we simply divide the total resistance by the length: R(meter) = 0.1 ohm / 10m = 0.01 ohm.
For the parallel combination with another wire of 0.250 ohms, we use the formula 1/R(total) = 1/R(1) + 1/R(2), where R(1) is the resistance of the first wire and R(2) is the resistance of the second wire. Substituting the values, we get 1/R(total) = 1/0.01 + 1/0.250 = 100 + 4 = 104. The total resistance is then R(total) = 1 / (1/104) = 0.00962 ohms.
To find the currents in each wire, we use Ohm's Law: I = V/R, where I is the current, V is the source current, and R is the resistance. For the first wire, I(1) = 6A * (0.00962 ohms / 0.1 ohm) = 0.5772A. For the second wire, I(2) = 6A * (0.00962 ohms / 0.250 ohms) = 0.23088A.