Answer:
Explanation:
Given that,
First wire has a resistance of
R1 = 0.1 Ω
We are told that
Second wire is twice as long as the first wire.
Then,
Let the first wire has length
L1 = x
Then, second wire will have
L2 = 2x
Also, the radius of the second wire is half the radius of the first wire
Let the first wire has radius
r1 = y
Then, it area is
A1 = πr1² = πy²
Then, the second wire has radius
r2 = ½y
It area is also
A2 = πr2² = π(½y)² = ½πy²
Since the wire is made of the same material, then, they will have the same resistivity ρ
Then, we want to find the resistance of the second wire
Using
R = ρL/A
Where
R = resistance
ρ = sensitivity
L = length
A = area
Then, make resistivity subject of formula since it is a constant
RA = ρL
Then, ρ = RA/L
Then,
R1 • A1 / L1 = R2 • A2 / L2
Substituting each value
0.1 × πy² / x = R2 × ¼πy² / 2x
Cross multiply
0.1 × πy² × 2x = R2 ×¼π y² × x
Then,
R2 = 0.1 × πy² × 2x / ¼πy² × x
R2 = 0.1 × 2 / ¼
R2 = 0.8Ω
The resistance of the second wire is 0.8Ω
