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If the length of a wire having uniform resistance R is stretched in m times with volume remaining same. What will be new resistance value?
- a)R/m
- b)Rm2
- c)mR
- d)R/m2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If the length of a wire having uniform resistance R is stretched in m ...
Given that, the length of a wire having uniform resistance R is stretched in m times with volume remaining same.
Let the length of the wire is L1
and the area of the wire is A1
For volume remains to be same
L1A1 = L2A2
⇒ L1A1 = (mL1) (A2)
⇒ A1 = mA2
Most Upvoted Answer
If the length of a wire having uniform resistance R is stretched in m ...
Understanding Resistance in a Stretched Wire
When a wire is stretched while keeping its volume constant, its length and cross-sectional area change, which affects its resistance.
Initial Parameters
- Let the original length of the wire be L.
- Let the original cross-sectional area be A.
- The original resistance is given by R = ρ(L/A), where ρ is the resistivity of the material.
Stretched Wire Characteristics
- If the wire is stretched by a factor of m, the new length (L') becomes L' = mL.
- Since the volume remains the same, the volume before stretching is equal to the volume after stretching: V = A * L = A' * L', where A' is the new cross-sectional area.
Volume Conservation
- Thus, A * L = A' * (mL).
- Rearranging gives A' = A / m.
New Resistance Calculation
- The new resistance (R') can be expressed as:
R' = ρ(L'/A').
- Substituting L' and A':
R' = ρ(mL / (A/m)) = ρ(m^2L/A).
Relating New Resistance to Original Resistance
- We can relate this to the original resistance:
R' = m^2 * (ρ(L/A)) = m^2 * R.
Final Result
- Therefore, the new resistance after stretching the wire is R' = m^2R.
The correct answer is option B) R/m², as it reflects the inverse relationship between resistance and the square of the stretching factor when volume remains constant.
When a wire is stretched while keeping its volume constant, its length and cross-sectional area change, which affects its resistance.
Initial Parameters
- Let the original length of the wire be L.
- Let the original cross-sectional area be A.
- The original resistance is given by R = ρ(L/A), where ρ is the resistivity of the material.
Stretched Wire Characteristics
- If the wire is stretched by a factor of m, the new length (L') becomes L' = mL.
- Since the volume remains the same, the volume before stretching is equal to the volume after stretching: V = A * L = A' * L', where A' is the new cross-sectional area.
Volume Conservation
- Thus, A * L = A' * (mL).
- Rearranging gives A' = A / m.
New Resistance Calculation
- The new resistance (R') can be expressed as:
R' = ρ(L'/A').
- Substituting L' and A':
R' = ρ(mL / (A/m)) = ρ(m^2L/A).
Relating New Resistance to Original Resistance
- We can relate this to the original resistance:
R' = m^2 * (ρ(L/A)) = m^2 * R.
Final Result
- Therefore, the new resistance after stretching the wire is R' = m^2R.
The correct answer is option B) R/m², as it reflects the inverse relationship between resistance and the square of the stretching factor when volume remains constant.
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