DSSSB TGT/PGT/PRT Exam > DSSSB TGT/PGT/PRT Questions > If a wire of resistance R is melted and recas...
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If a wire of resistance R is melted and recasted to a wire of half of its length, then the new resistance of the wire will be
- a)R/4
- b)R/2
- c)R
- d)2R
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If a wire of resistance R is melted and recasted to a wire of half of ...
Understanding Resistance
Resistance (R) of a wire is determined by the formula:
- R = ρ * (L/A)
where:
- ρ = resistivity of the material
- L = length of the wire
- A = cross-sectional area of the wire
When the wire is melted and recast, the volume remains constant.
Volume of the Wire
The volume (V) of the wire can be expressed as:
- V = L * A
For the original wire:
- V1 = L1 * A1
For the new wire of half the length:
- V2 = (L1/2) * A2
Since the volume is conserved, we have:
- L1 * A1 = (L1/2) * A2
This simplifies to:
- A2 = 2 * A1
New Resistance Calculation
Now, we substitute A2 into the resistance formula for the new wire:
- R_new = ρ * (L2/A2)
- R_new = ρ * ((L1/2) / (2 * A1))
- R_new = ρ * (L1 / (4 * A1))
Comparing this with the original resistance (R):
- R = ρ * (L1/A1)
Thus, we find:
- R_new = R/4
Conclusion
Therefore, the new resistance of the recast wire, which is half the length of the original wire, is:
- R/4
The correct answer is option 'A'.
Resistance (R) of a wire is determined by the formula:
- R = ρ * (L/A)
where:
- ρ = resistivity of the material
- L = length of the wire
- A = cross-sectional area of the wire
When the wire is melted and recast, the volume remains constant.
Volume of the Wire
The volume (V) of the wire can be expressed as:
- V = L * A
For the original wire:
- V1 = L1 * A1
For the new wire of half the length:
- V2 = (L1/2) * A2
Since the volume is conserved, we have:
- L1 * A1 = (L1/2) * A2
This simplifies to:
- A2 = 2 * A1
New Resistance Calculation
Now, we substitute A2 into the resistance formula for the new wire:
- R_new = ρ * (L2/A2)
- R_new = ρ * ((L1/2) / (2 * A1))
- R_new = ρ * (L1 / (4 * A1))
Comparing this with the original resistance (R):
- R = ρ * (L1/A1)
Thus, we find:
- R_new = R/4
Conclusion
Therefore, the new resistance of the recast wire, which is half the length of the original wire, is:
- R/4
The correct answer is option 'A'.
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Community Answer
If a wire of resistance R is melted and recasted to a wire of half of ...
The resistance (R) of a wire is directly proportional to its length (L) and inversely proportional to its cross-sectional area (A). This is given by the equation R = ρL/A, where ρ is the resistivity of the material of the wire.
- When the wire is melted and recast into a new wire with half its original length, two things happen:
- The length (L) of the wire is halved.
- The volume of the wire remains the same. Since the volume (V) of a wire is given by the product of its length (L) and its cross-sectional area (A), i.e., V = L*A, if the length is halved, the cross-sectional area must have doubled to maintain the same volume.
Calculating the New Resistance
The new resistance (R') of the wire can be calculated using the same formula: R' = ρL'/A', where L' is the new length and A' is the new cross-sectional area.
Substituting the new values:
The new resistance (R') of the wire can be calculated using the same formula: R' = ρL'/A', where L' is the new length and A' is the new cross-sectional area.
Substituting the new values:
- L' = L/2 (since the length is halved)
- A' = 2A (since the cross-sectional area is doubled)
The equation becomes R' = ρ(L/2)/(2A) = ρL/(4A) = R/4 (since ρL/A = R)
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