Hi there!
a)
We know that the resistance of the wire is equivalent to:
[tex]R = \frac{\rho L}{A}[/tex]
R = Resistance (Ω)
ρ = Resistivity (Ωm)
L = Length (m)
A = Cross-sectional area (m²)
We can relate the voltage to an electric field by:
[tex]V = Ed \\\\V = El[/tex]
V = Potential Difference (V)
E = Electric Field (V/m)
l = Length of wire (m)
And Ohm's Law:
[tex]V =iR[/tex]
i = Current (A)
V = Potential Difference (V)
R = Resistance (Ω)
We do not know the length, so we can solve using the above relationships.
[tex]V = iR\\\\V = i\frac{\rho L}{A}\\\\\frac{V}{L} = E = i\frac{\rho}{A}\\\\i = \frac{EA}{\rho} = \frac{.55 \times \pi (0.00044^2)}{(2.44 \times 10^{-8})}} = \boxed{13.71 A}[/tex]
b)
We know that V = Ed (Electric field × distance), so:
[tex]V = 0.55 \times 6.3 = \boxed{3.465 V}[/tex]
c)
Calculate the resistance using the above equation.
[tex]R = \frac{\rho L}{A}\\\\R = \frac{(2.44\times 10^{-8})(6.3)}{\pi(0.044^2)} = \boxed{2.527 \times 10^{-5} \Omega}[/tex]
