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A metal wire of resistance R is cut into three equal pieces which are then connected side by side to form a new wire, the length of which is equal to one third of the original length. the resistance of the new wire will be ?
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A metal wire of resistance R is cut into three equal pieces which are ...
Your question seems incorrect. There is a contradiction in your question. If three pieces of wire are connected side by side it means they are connected in series combination and if the length of new wire formed is one third of the original wire then three pieces must be connected in parallel combination to satisfy this condition.
I am providing you answer of both the cases.
The metal wire is cut into three equal pieces.
Let the original length of the wire be l
=> length of each of the three wires, l' = l/3
resistance of the original wire, R = ρl/A
Resistance of each of the wire, R' = R/3
Now as the three wires are connected side by side, that is, in series then
The total resistance R''= R' + R' + R'
= 3R'
= R
But if the wires are connected in parallel( the new wire is one third of the original length), then
the length of each wire, l' = l/3
resistance of each wire, R'= R/3
total resistance of the arrangement, R'' = R'/3 =R/9
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Most Upvoted Answer
A metal wire of resistance R is cut into three equal pieces which are ...
Answer:
Given information:
- Original wire resistance: R
- Original wire length: L
- Wire is cut into three equal pieces.
- Pieces are connected side by side to form a new wire.
- Length of the new wire = L/3
Explanation:
1. Resistance of each piece:
When the original wire is cut into three equal pieces, each piece will have the same resistance as the original wire. This is because resistance is a property of the material and is independent of the length or shape of the wire. So, the resistance of each piece will be R.
2. Connection of the pieces:
The three equal pieces are connected side by side to form a new wire. When wires are connected in this manner, their resistances add up. Therefore, the resistance of the new wire will be equal to the sum of the resistances of the three equal pieces.
3. Length of the new wire:
The length of the new wire is equal to one third of the original length. Let's denote the original length as L. So, the length of the new wire will be L/3.
4. Calculation of the resistance of the new wire:
Since the resistance of each piece is R, and the new wire is formed by connecting three equal pieces, the resistance of the new wire will be equal to 3R. This is because the resistances add up when connected in this manner.
5. Summary:
- Original wire resistance: R
- Original wire length: L
- Resistance of each piece: R
- Length of the new wire: L/3
- Resistance of the new wire: 3R
Conclusion:
The resistance of the new wire formed by connecting three equal pieces of the original wire side by side will be 3 times the resistance of each piece, or 3R.
Given information:
- Original wire resistance: R
- Original wire length: L
- Wire is cut into three equal pieces.
- Pieces are connected side by side to form a new wire.
- Length of the new wire = L/3
Explanation:
1. Resistance of each piece:
When the original wire is cut into three equal pieces, each piece will have the same resistance as the original wire. This is because resistance is a property of the material and is independent of the length or shape of the wire. So, the resistance of each piece will be R.
2. Connection of the pieces:
The three equal pieces are connected side by side to form a new wire. When wires are connected in this manner, their resistances add up. Therefore, the resistance of the new wire will be equal to the sum of the resistances of the three equal pieces.
3. Length of the new wire:
The length of the new wire is equal to one third of the original length. Let's denote the original length as L. So, the length of the new wire will be L/3.
4. Calculation of the resistance of the new wire:
Since the resistance of each piece is R, and the new wire is formed by connecting three equal pieces, the resistance of the new wire will be equal to 3R. This is because the resistances add up when connected in this manner.
5. Summary:
- Original wire resistance: R
- Original wire length: L
- Resistance of each piece: R
- Length of the new wire: L/3
- Resistance of the new wire: 3R
Conclusion:
The resistance of the new wire formed by connecting three equal pieces of the original wire side by side will be 3 times the resistance of each piece, or 3R.
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A metal wire of resistance R is cut into three equal pieces which are then connected side by side to form a new wire, the length of which is equal to one third of the original length. the resistance of the new wire will be ?
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A metal wire of resistance R is cut into three equal pieces which are then connected side by side to form a new wire, the length of which is equal to one third of the original length. the resistance of the new wire will be ? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A metal wire of resistance R is cut into three equal pieces which are then connected side by side to form a new wire, the length of which is equal to one third of the original length. the resistance of the new wire will be ? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metal wire of resistance R is cut into three equal pieces which are then connected side by side to form a new wire, the length of which is equal to one third of the original length. the resistance of the new wire will be ?.
A metal wire of resistance R is cut into three equal pieces which are then connected side by side to form a new wire, the length of which is equal to one third of the original length. the resistance of the new wire will be ? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A metal wire of resistance R is cut into three equal pieces which are then connected side by side to form a new wire, the length of which is equal to one third of the original length. the resistance of the new wire will be ? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metal wire of resistance R is cut into three equal pieces which are then connected side by side to form a new wire, the length of which is equal to one third of the original length. the resistance of the new wire will be ?.
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