Question

A metal wire of resistance 6ohm is stretched to twice of its original length. Calculate its new resistance.

Answer 1

Original length of wire= l1

New length of wire =2l1

Reistance of wire =R1=6 ohms

Resistance of new wire=?

we know that :

R1=ρ l1/A1-----------------1

When length is doubled  

Volume of wire remains same :

A1x 11= A2x l2

l2=2l1

so

A1xl1=A2x2lx1

A2=A1/2 -------------2

R2=ρ l2/A2

R2=ρ[2l1/A1/2

]

R2=4[ρl1/A1] [ from equation 1]

R2= 4xR1

=4x6=24ohms