Question

two copper wires x and y have the same volume. wire y is four times as long as wire x.
what is ratio of
Resistance of wire Y /
Resistance of wire X​

Answer 1

Hint: Find the ratio between the areas of the two copper wires as length is given and we know the volumes of both wires are equal. Resistance

depends on the resistivity, area and length of the wires. As we know, all the terms, we can find the ratio easily.

Formula used:

V=A×lR=ρlA

Complete answer:

Let us first find the relation between the areas of the two copper wires. We know, the volumes of both the copper wires is same and the relation between length is given,

Now,

V=A×l⇒Ax×lx=Ay×ly⇒Ax×L=Ay×4L⇒AxAy=4

Now, we know the relation between the areas of the copper wires, length of the copper wires. The resistivity for two copper wires is same because the two wires are made of same material.

Therefore,

R=ρlA⇒R1=ρLAx⇒R2=ρ×4LAy⇒R1R2=ρLAxρ×4LAy⇒R1R2=Ay4×Ax⇒R1R2=116⇒R2R1=16