Two wires of circular cross section are made of the same metal. Wire 1 has radius rr and length LL; wire 2 has radius 2r2r and length 2L2L. The potential difference between the ends of the wire is the same for both wires. Find the ratio of the resistance of wire 2 to the resistance of wire 1.

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

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 =

therefore,

resistance R =

For the second wire 2

cross sectional area =

therefore,

resistance R =

Ratio of wire 2 to wire 1 will be

÷ = x

Ratio of resistance of wire 2 to wire 1 = 2/4 = 0.5 : 1

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