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Resistance of a wire is R . A part of its length is stretched so that it's total length become 1.5 times of initial length.If new resistance of wire is 3R then find the length of the part that is stretched.?
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Resistance of a wire is R . A part of its length is stretched so that ...
Let's consider the initial length of the wire as L and its resistance as R.
The formula for resistance of a wire is given by:
R = ρ * (L/A)
where R is the resistance, ρ is the resistivity of the wire material, L is the length of the wire, and A is the cross-sectional area of the wire.
Now, a part of the wire is stretched, making its total length 1.5 times the initial length. Let's denote the length of the stretched part as x.
The length of the unstretched part of the wire would be (L - x).
According to the question, the new resistance of the wire after stretching is 3R.
So, we can write the new resistance as:
3R = ρ * [(L-x)/A + x/A]
Simplifying the equation, we get:
3R = ρ * [(L-x+x)/A]
3R = ρ * (L/A)
3R = R
From the above equation, we can see that the new resistance is 3 times the initial resistance.
Now, let's solve for x, the length of the stretched part:
3R = R
3 = 1 + x/(L - x)
Cross-multiplying, we get:
3(L - x) = L - x
3L - 3x = L - x
Simplifying the equation, we get:
2L = 2x
L = x
Therefore, the length of the part that is stretched is equal to the length of the unstretched part, which means that the entire wire is stretched uniformly.
In conclusion, if the new resistance of the wire after stretching is 3R, then the length of the part that is stretched is equal to the length of the unstretched part.
The formula for resistance of a wire is given by:
R = ρ * (L/A)
where R is the resistance, ρ is the resistivity of the wire material, L is the length of the wire, and A is the cross-sectional area of the wire.
Now, a part of the wire is stretched, making its total length 1.5 times the initial length. Let's denote the length of the stretched part as x.
The length of the unstretched part of the wire would be (L - x).
According to the question, the new resistance of the wire after stretching is 3R.
So, we can write the new resistance as:
3R = ρ * [(L-x)/A + x/A]
Simplifying the equation, we get:
3R = ρ * [(L-x+x)/A]
3R = ρ * (L/A)
3R = R
From the above equation, we can see that the new resistance is 3 times the initial resistance.
Now, let's solve for x, the length of the stretched part:
3R = R
3 = 1 + x/(L - x)
Cross-multiplying, we get:
3(L - x) = L - x
3L - 3x = L - x
Simplifying the equation, we get:
2L = 2x
L = x
Therefore, the length of the part that is stretched is equal to the length of the unstretched part, which means that the entire wire is stretched uniformly.
In conclusion, if the new resistance of the wire after stretching is 3R, then the length of the part that is stretched is equal to the length of the unstretched part.
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Resistance of a wire is R . A part of its length is stretched so that it's total length become 1.5 times of initial length.If new resistance of wire is 3R then find the length of the part that is stretched.?
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Resistance of a wire is R . A part of its length is stretched so that it's total length become 1.5 times of initial length.If new resistance of wire is 3R then find the length of the part that is stretched.? 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 Resistance of a wire is R . A part of its length is stretched so that it's total length become 1.5 times of initial length.If new resistance of wire is 3R then find the length of the part that is stretched.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Resistance of a wire is R . A part of its length is stretched so that it's total length become 1.5 times of initial length.If new resistance of wire is 3R then find the length of the part that is stretched.?.
Resistance of a wire is R . A part of its length is stretched so that it's total length become 1.5 times of initial length.If new resistance of wire is 3R then find the length of the part that is stretched.? 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 Resistance of a wire is R . A part of its length is stretched so that it's total length become 1.5 times of initial length.If new resistance of wire is 3R then find the length of the part that is stretched.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Resistance of a wire is R . A part of its length is stretched so that it's total length become 1.5 times of initial length.If new resistance of wire is 3R then find the length of the part that is stretched.?.
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