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?

Check all that apply.
A. Wire B has twice the resistance of wire A. Wire B has twice the resistivity of wire A.
B. Wire A has twice the resistance of wire B. Wire A and wire B have the same resistivity.
C. Wire A and wire B have the same resistance.
D. Wire A has twice the resistivity of wire B.

Answer 1

Answer:

Wire A has wire resistance as wire B and both wire have resistivity

So option is B is correct answer                  

Explanation:

We have given that wire A has twice the length as of wire B $l_A=2l_B$

And area of cross section is same so $A_a=A_b$

We know that resistance is given by $R=\frac{\rho l}{A}$

So $R_a=\frac{\rho l_a}{A_a}$ and $R_b=\frac{\rho l_b}{A_b}$

From the resistance expression we can see that resistance is directly proportional to length

As $l_A=2l_B$

So resistance of wire A is twice the resistance of wire B

And as both the wire is made up of copper so resitivity will be same

So option B will be correct option