Answer:
Ratio of wire 2 to wire 1 is 0.5 : 1
Explanation:
Wire 1:
length = L
radius = r
Wire 2:
length = 2L
radius = 2r
Resistance of a conductor varies directly as the length and inversely as the cross sectional area. Mathematically
[tex]R = \frac{pl}{a}[/tex]
l = length of conductor
a = cross sectional area of the conductor
p = resistivity of the material with which the conductor is made.
since we are considering the same material, we can ignore the resistivity of the wire.
For wire 1
cross sectional area = [tex]\pi r^{2}[/tex]
therefore,
resistance R = [tex]\frac{L}{\pi r^{2} }[/tex]
For the second wire 2
cross sectional area = [tex]4\pi r^{2}[/tex]
therefore,
resistance R = [tex]\frac{2L}{4\pi r^{2} }[/tex]
Ratio of wire 2 to wire 1 will be
[tex]\frac{2L}{4\pi r^{2} }[/tex] ÷ [tex]\frac{L}{\pi r^{2} }[/tex] = [tex]\frac{2L}{4\pi r^{2} }[/tex] x [tex]\frac{\pi r^{2} }{L}[/tex]
Ratio of resistance of wire 2 to wire 1 = 2/4 = 0.5 : 1
