Question

Consider two copper wires with the same cross-sectional area. Wire a is twice as long as wire b. How do the resistivities and resistances of the two wires compare?

Answer 1

Answer:

from the equation 1 below, the ratio of the resistivity of wire b to its resistance is twice the ratio of the resistivity if wire A to its resistance.

Explanation:

R=(ρL)/A

A =(ρL)/R

Where A is cross sectional area,

ρ is the resistivity

L is length of wire

R is resistance of wire.

from the question the two wires have same cross sectional area.

Aa =Ab  ; hence

(ρaLa)/Ra  = (ρbLb)/Rb

La =2Lb

(ρa*2Lb)/Ra  = (ρbLb)/Rb

(2ρa)/Ra  = (ρb)/Rb

ρb/Rb  =  2* ρa/Ra        ...................                equ 1