Answer:
42 m
Explanation:
From ohm's law,
V = IR............... Equation 1
Where V = Voltage, I = current, R = Resistance.
Make R the subject of the equation
R = V/I............. Equation 2
Given: V = 1.5 V, I = 0.40 A.
Substitute into equation 2
R = 1.5/0.4
R = 3.75 Ω.
But,
R = ρL/A..............Equation 2
Where ρ = resistivity of the aluminum wire, l = length of the wire, A = cross sectional area of the wire.
make L the subject of the equation,
L = RA/ρ..............Equation 3
Given: R = 3.75 Ω,
A = πd²/4, where d = diameter = 0.62 mm = 0.00062 m, π = 3.14
A = 3.14× 0.00062²/4 = 0.000000302 m²
Constant: ρ = 2.65 × 10⁻⁸ Ω·m
Substitute into equation 3
L = 3.75(0.000000302)/(2.65 × 10⁻⁸ )
L = 3.75(3.02×10⁻⁷)/(2.65 × 10⁻⁸)
L = 42.70 m
L = 42 m ( Two significant figures)
