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Two metallic wires A and B are made using copper. The radius of wire A is r while its length is I. A dc voltage V is applied across the wire A, causing power dissipation P. The radius of wire B is 2r and its length is 2I and the same dc voltage V is applied across it causing power dissipation P1 . Which one of the following is the correct relationship between P and P1?
- a)P= P1/2
- b)P= 2P1
- c)P= 4P1
- d)P= P1
Correct answer is option 'B'. Can you explain this answer?
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Two metallic wires A and B are made using copper. The radius of wire A...
Resistance of a wire,
If Ro is the resistance of first wire, the resistance of second wire.
This question is part of UPSC exam. View all Defence courses
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Two metallic wires A and B are made using copper. The radius of wire A...
Given:
- Wire A has radius r and length I.
- Wire B has radius 2r and length 2I.
- Both wires are made of copper.
- A dc voltage V is applied across both wires.
- Wire A dissipates power P.
- Wire B dissipates power P1.
To find: The relationship between P and P1.
Explanation:
1. Power dissipation in a wire can be calculated using the formula:
P = (V^2 * R) / I
where V is the voltage, R is the resistance, and I is the current.
2. The resistance of a wire depends on its length, cross-sectional area, and resistivity of the material. The resistance can be calculated using the formula:
R = (ρ * L) / A
where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area.
3. Since both wires are made of copper, they have the same resistivity (ρ) value.
4. Cross-sectional area (A) is directly proportional to the square of the radius (r^2). Therefore, the cross-sectional area of wire B is 4 times that of wire A.
5. Length (L) of wire B is twice that of wire A.
6. Substituting the values of resistance and voltage in the power dissipation formula, we get:
P = (V^2 * (ρ * I) / (r^2)) (for wire A)
P1 = (V^2 * (ρ * 2I) / ((2r)^2)) (for wire B)
7. Simplifying the above equations, we have:
P = (V^2 * ρ * I) / (r^2)
P1 = (V^2 * ρ * 2I) / (4r^2)
= (V^2 * ρ * I) / (2r^2)
8. Comparing P and P1, we can see that P1 is equal to half of P.
Therefore, the correct relationship between P and P1 is:
P = 2P1 (option b).
Therefore, the correct answer is option b) P = 2P1.
- Wire A has radius r and length I.
- Wire B has radius 2r and length 2I.
- Both wires are made of copper.
- A dc voltage V is applied across both wires.
- Wire A dissipates power P.
- Wire B dissipates power P1.
To find: The relationship between P and P1.
Explanation:
1. Power dissipation in a wire can be calculated using the formula:
P = (V^2 * R) / I
where V is the voltage, R is the resistance, and I is the current.
2. The resistance of a wire depends on its length, cross-sectional area, and resistivity of the material. The resistance can be calculated using the formula:
R = (ρ * L) / A
where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area.
3. Since both wires are made of copper, they have the same resistivity (ρ) value.
4. Cross-sectional area (A) is directly proportional to the square of the radius (r^2). Therefore, the cross-sectional area of wire B is 4 times that of wire A.
5. Length (L) of wire B is twice that of wire A.
6. Substituting the values of resistance and voltage in the power dissipation formula, we get:
P = (V^2 * (ρ * I) / (r^2)) (for wire A)
P1 = (V^2 * (ρ * 2I) / ((2r)^2)) (for wire B)
7. Simplifying the above equations, we have:
P = (V^2 * ρ * I) / (r^2)
P1 = (V^2 * ρ * 2I) / (4r^2)
= (V^2 * ρ * I) / (2r^2)
8. Comparing P and P1, we can see that P1 is equal to half of P.
Therefore, the correct relationship between P and P1 is:
P = 2P1 (option b).
Therefore, the correct answer is option b) P = 2P1.
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Two metallic wires A and B are made using copper. The radius of wire A is r while its length is I. A dc voltage V is applied across the wire A, causing power dissipation P. The radius of wire B is 2r and its length is 2I and the same dc voltage V is applied across it causing power dissipation P1 . Which one of the following is the correct relationship between P and P1?a)P= P1/2b)P= 2P1c)P= 4P1d)P= P1Correct answer is option 'B'. Can you explain this answer?
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Two metallic wires A and B are made using copper. The radius of wire A is r while its length is I. A dc voltage V is applied across the wire A, causing power dissipation P. The radius of wire B is 2r and its length is 2I and the same dc voltage V is applied across it causing power dissipation P1 . Which one of the following is the correct relationship between P and P1?a)P= P1/2b)P= 2P1c)P= 4P1d)P= P1Correct answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Two metallic wires A and B are made using copper. The radius of wire A is r while its length is I. A dc voltage V is applied across the wire A, causing power dissipation P. The radius of wire B is 2r and its length is 2I and the same dc voltage V is applied across it causing power dissipation P1 . Which one of the following is the correct relationship between P and P1?a)P= P1/2b)P= 2P1c)P= 4P1d)P= P1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two metallic wires A and B are made using copper. The radius of wire A is r while its length is I. A dc voltage V is applied across the wire A, causing power dissipation P. The radius of wire B is 2r and its length is 2I and the same dc voltage V is applied across it causing power dissipation P1 . Which one of the following is the correct relationship between P and P1?a)P= P1/2b)P= 2P1c)P= 4P1d)P= P1Correct answer is option 'B'. Can you explain this answer?.
Two metallic wires A and B are made using copper. The radius of wire A is r while its length is I. A dc voltage V is applied across the wire A, causing power dissipation P. The radius of wire B is 2r and its length is 2I and the same dc voltage V is applied across it causing power dissipation P1 . Which one of the following is the correct relationship between P and P1?a)P= P1/2b)P= 2P1c)P= 4P1d)P= P1Correct answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Two metallic wires A and B are made using copper. The radius of wire A is r while its length is I. A dc voltage V is applied across the wire A, causing power dissipation P. The radius of wire B is 2r and its length is 2I and the same dc voltage V is applied across it causing power dissipation P1 . Which one of the following is the correct relationship between P and P1?a)P= P1/2b)P= 2P1c)P= 4P1d)P= P1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two metallic wires A and B are made using copper. The radius of wire A is r while its length is I. A dc voltage V is applied across the wire A, causing power dissipation P. The radius of wire B is 2r and its length is 2I and the same dc voltage V is applied across it causing power dissipation P1 . Which one of the following is the correct relationship between P and P1?a)P= P1/2b)P= 2P1c)P= 4P1d)P= P1Correct answer is option 'B'. Can you explain this answer?.
Solutions for Two metallic wires A and B are made using copper. The radius of wire A is r while its length is I. A dc voltage V is applied across the wire A, causing power dissipation P. The radius of wire B is 2r and its length is 2I and the same dc voltage V is applied across it causing power dissipation P1 . Which one of the following is the correct relationship between P and P1?a)P= P1/2b)P= 2P1c)P= 4P1d)P= P1Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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