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A copper wire is stretched to double its length keeping the volume seen if the original resistance of the wire is 4 ohm what is the final resistance?
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A copper wire is stretched to double its length keeping the volume see...
Understanding Resistance in a Stretched Wire
When a copper wire is stretched to double its length while keeping its volume constant, its resistance changes. Let’s analyze this phenomenon step by step.
Initial Resistance
- The original resistance (R1) of the wire is given as 4 ohms.
Volume Conservation
- When the wire is stretched to double its length (L), the volume (V) remains constant.
- Volume formula: V = A × L (where A is the cross-sectional area).
Effects of Stretching
- When the length is doubled (L becomes 2L), the volume remains constant:
- A1 × L = A2 × 2L
- This implies A2 = A1/2, indicating that the cross-sectional area is halved.
Resistance Formula
- Resistance (R) is given by the formula:
R = ρ × (L/A)
where ρ is the resistivity of the material, L is the length, and A is the cross-sectional area.
Calculating Final Resistance
- With the new length (2L) and new area (A1/2):
R2 = ρ × (2L/(A1/2))
R2 = ρ × (4L/A1)
- Given that R1 = ρ × (L/A1) = 4 ohms, we can substitute:
R2 = 4 × 4 = 16 ohms.
Final Result
- The final resistance of the stretched wire is 16 ohms.
This demonstrates how stretching a wire affects its resistance due to changes in length and cross-sectional area while conserving volume.
When a copper wire is stretched to double its length while keeping its volume constant, its resistance changes. Let’s analyze this phenomenon step by step.
Initial Resistance
- The original resistance (R1) of the wire is given as 4 ohms.
Volume Conservation
- When the wire is stretched to double its length (L), the volume (V) remains constant.
- Volume formula: V = A × L (where A is the cross-sectional area).
Effects of Stretching
- When the length is doubled (L becomes 2L), the volume remains constant:
- A1 × L = A2 × 2L
- This implies A2 = A1/2, indicating that the cross-sectional area is halved.
Resistance Formula
- Resistance (R) is given by the formula:
R = ρ × (L/A)
where ρ is the resistivity of the material, L is the length, and A is the cross-sectional area.
Calculating Final Resistance
- With the new length (2L) and new area (A1/2):
R2 = ρ × (2L/(A1/2))
R2 = ρ × (4L/A1)
- Given that R1 = ρ × (L/A1) = 4 ohms, we can substitute:
R2 = 4 × 4 = 16 ohms.
Final Result
- The final resistance of the stretched wire is 16 ohms.
This demonstrates how stretching a wire affects its resistance due to changes in length and cross-sectional area while conserving volume.
Community Answer
A copper wire is stretched to double its length keeping the volume see...
16ohm
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A copper wire is stretched to double its length keeping the volume seen if the original resistance of the wire is 4 ohm what is the final resistance?
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A copper wire is stretched to double its length keeping the volume seen if the original resistance of the wire is 4 ohm what is the final resistance? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A copper wire is stretched to double its length keeping the volume seen if the original resistance of the wire is 4 ohm what is the final resistance? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A copper wire is stretched to double its length keeping the volume seen if the original resistance of the wire is 4 ohm what is the final resistance?.
A copper wire is stretched to double its length keeping the volume seen if the original resistance of the wire is 4 ohm what is the final resistance? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A copper wire is stretched to double its length keeping the volume seen if the original resistance of the wire is 4 ohm what is the final resistance? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A copper wire is stretched to double its length keeping the volume seen if the original resistance of the wire is 4 ohm what is the final resistance?.
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