Question

Masses of copper wires are in ratio 1:3:5 and lengths of ratio 5:3:1 . Whats the ratio of their electrical resistances ?

Answer 1

mass ratio of 3 wires
1 : 3 : 5

lengths are in ratio
5 : 3: 1

V = A * L

V = pi*r^2 * L

density = d

m = V*d

m = A*L * d

A = m/(L *d)

R = p*L/A

p is constant for all copper so now we just have to find the ratio of L to area
since d = density of copper it is constant too .. so the only variables are

A varies m/L



R varies L/A

R varies by L/ (m/L)

R varies by L*L/m

R varies by L^2/m

first wire

R1 = 5^2/1 = 25

R2 = 3^2/3 = 3

R3 = 1^2/5 = 1/5

the resistance vary by

25 : 3: 1/5

or

125 : 15 : 1

I multiplied by 5 through the whole thing
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