If the length and diameter of a copper wire connected to a b

If the length and diameter of a copper wire connected to a battery are doubled, state whether the following quantities will increase, decrease, or stay the same. (The connection to the battery means that a constant potential difference Ls maintained between the ends of the wire.) Resistivity of the wire. Resistance of the wire. Current in the wire. Current density in the wire. (Assume the current density is uniform throughout the wire.)

Solution

a)

Stays the same ,since resistivity of the wire is constant

b)

Decreases ,since

Resistance of a wire is given by

R=pL/A

Now Given L_new=2L and Diameter

d_new=2d

A_new =pi*d_new²/4 =pi*(2d)²/4 =4A

So new resistance is

R_new =p*(2L)/(4A) =(1/2)(pL/A)

R_new =(1/2)R

c)

Increases ,since

Current in the wire is given by

I=V/R

Now new current

I_new=V/(R/2)=2(V/R)

I_new=2I

d)

Decreases ,since

Current density

J=I/A

New current density

J_new =I_new/A_new=2I/4A

J_new =(1/2)J