Answer:
L = 30.85 m
Explanation:
First, we calculate the resistance of the wire by using Ohm's Law:
V = IR
where,
V = Potential Difference = 1.5 V
I = Current = 0.42 A
R = Resistance of Wire = ?
Therefore,
[tex]R = \frac{1.5\ V}{0.42\ A}\\\\R = 3.57\ Ohms[/tex]
Now, the cross-sectional area of wire will be:
[tex]Area = A = \frac{\pi d^{2}}{4}\\\\A = \frac{\pi (0.00054\ m)^{2}}{4}\\\\A = 2.29\ x\ 10^{-7}\ m^{2}[/tex]
Now, the resistance of the wire is given as:
[tex]R = \frac{\rho L}{A}\\\\L = \frac{RA}{\rho}[/tex]
where,
L = Length of Wire = ?
ρ = resistivity of aluminum = 2.65×10⁻⁸ Ohm.m
Therefore,
[tex]L = \frac{(3.57\ Ohms)(2.29\ x\ 10^{-7}\ m^{2})}{2.65\ x\ 10^{-8}\ Ohm.m}[/tex]
L = 30.85 m
