To calculate the new resistance after the wire is stretched, we need to use the fact that resistance is proportional to the length and inversely proportional to the cross-sectional area of the wire. The formula for resistance is given by:
R=ρwhere
ρ is the resistivity of the material,
L is the length, and
A is the cross-sectional area.
Initially, the length of the wire is 10 m and the resistance is
10Ω. When the length is increased by
25%, the new length becomes:
Lnew =10m+(0.25×10m)=12.5mLet's denote the initial resistance as
Rinitial =10Ω and the initial length as
Linitial =10m.
The volume of the wire remains constant during stretching, so:
Linitial ×Ainitial =Lnew ×Anew This implies:
10m×Ainitial =12.5m×Anew So,
Anew ==0.8×Ainitial The new resistance is calculated as:
Rnew =ρ Using the relationship between initial and final conditions, we get:
Since
Rinitial =ρ, we can write:
Rnew =1.25×Rinitial × Substitute the known values:
Rnew =1.25×10Ω×Simplify:
Rnew =1.25×10Ω×1.25Rnew =1.5625×10ΩRnew =15.625ΩRounding it to one decimal place,
Rnew ≈15.6Ω.
Therefore, the new resistance is Option B:
15.6Ω.