Question
Physics Question on Current electricity
A wire of resistance 2R is stretched such that its length is doubled. Then the increase in its resistance is:
A
6R
B
4R
C
3R
D
2R
Answer
6R
Explanation
Solution
The correct option is: (A) : 6R
R = ρ * (L / A)
Where:
- R is resistance
- ρ is resistivity of the material
- L is the length of the wire
- A is the cross-sectional area of the wire
Since the wire's length is doubled, the new length becomes 2L. However, its cross-sectional area doesn't change due to stretching. So the new resistance (R_new) can be expressed as:
R_new = ρ * (2L / A)
The increase in resistance (ΔR) is the difference between the new resistance and the initial resistance:
ΔR = R_new - R ΔR = ρ * (2L / A) - ρ * (L / A) ΔR = ρ * (2L - L) / A ΔR = ρ * L / A
Now, since the initial resistance was 2R, we can equate ΔR to 6R:
ρ * L / A = 6R