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A wire of length L and 3 identical cells, of negligible internal resistance, are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time. Find the value of N.
Correct answer is '6'. Can you explain this answer?
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Most Upvoted Answer
A wire of length L and 3 identical cells, of negligible internal resi...
Understanding the Problem
In the first scenario, a wire of length L is connected to 3 identical cells in series, leading to a temperature increase of ΔT in time t.
Heat Produced in the Wire
- The heat produced in the wire can be calculated using the formula:
Q = I^2Rt
- Here, Q is the heat produced, I is the current, R is the resistance of the wire, and t is the time.
Resistance of the Wire
- The resistance R of the wire is given by:
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.
Current Calculation
- The total voltage (V) across the 3 cells is:
V = 3V_cell
- The current I flowing through the wire is:
I = V/R = (3V_cell * A)/(ρL)
Second Scenario with N Cells
In the second scenario, N identical cells are connected in series with a wire of length 2L.
Heat Production in the Second Wire
- The resistance R' of the second wire is:
R' = ρ(2L/A) = 2R
- The total voltage (V') across N cells is:
V' = NV_cell
- The current I' in this case becomes:
I' = V'/R' = (NV_cell)/(2R)
Equalizing Heat Production
- For the same temperature increase ΔT in the same time t, set the heat produced in both wires equal:
I^2Rt = (I')^2R't
- Substituting the values, we find:
(3V_cell/AρL)^2 * R * t = (NV_cell/(2R))^2 * 2R * t
Simplifying the Equation
- Cancel t and simplify:
9/(L^2) = N^2/(4R^2)
- This leads to:
N^2 = 36
Conclusion
- Solving gives N = 6. Thus, the number of cells required is N = 6.
In the first scenario, a wire of length L is connected to 3 identical cells in series, leading to a temperature increase of ΔT in time t.
Heat Produced in the Wire
- The heat produced in the wire can be calculated using the formula:
Q = I^2Rt
- Here, Q is the heat produced, I is the current, R is the resistance of the wire, and t is the time.
Resistance of the Wire
- The resistance R of the wire is given by:
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.
Current Calculation
- The total voltage (V) across the 3 cells is:
V = 3V_cell
- The current I flowing through the wire is:
I = V/R = (3V_cell * A)/(ρL)
Second Scenario with N Cells
In the second scenario, N identical cells are connected in series with a wire of length 2L.
Heat Production in the Second Wire
- The resistance R' of the second wire is:
R' = ρ(2L/A) = 2R
- The total voltage (V') across N cells is:
V' = NV_cell
- The current I' in this case becomes:
I' = V'/R' = (NV_cell)/(2R)
Equalizing Heat Production
- For the same temperature increase ΔT in the same time t, set the heat produced in both wires equal:
I^2Rt = (I')^2R't
- Substituting the values, we find:
(3V_cell/AρL)^2 * R * t = (NV_cell/(2R))^2 * 2R * t
Simplifying the Equation
- Cancel t and simplify:
9/(L^2) = N^2/(4R^2)
- This leads to:
N^2 = 36
Conclusion
- Solving gives N = 6. Thus, the number of cells required is N = 6.
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Community Answer
A wire of length L and 3 identical cells, of negligible internal resi...
In the first case,
(3E)2 / Rt = msΔT ... (i)
When the length of the wire is doubled, resistance and mass both are doubled. Therefore, in the second case,
(NE)2 / 2R x t = (2m)sΔT ... (ii)
Dividing Eq.(ii) by (i) we get,
N2 / 18 = 2
or N2 = 36
or N = 6
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A wire of length L and 3 identical cells, of negligible internal resistance, are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time. Find the value of N.Correct answer is '6'. Can you explain this answer?
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A wire of length L and 3 identical cells, of negligible internal resistance, are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time. Find the value of N.Correct answer is '6'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A wire of length L and 3 identical cells, of negligible internal resistance, are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time. Find the value of N.Correct answer is '6'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of length L and 3 identical cells, of negligible internal resistance, are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time. Find the value of N.Correct answer is '6'. Can you explain this answer?.
A wire of length L and 3 identical cells, of negligible internal resistance, are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time. Find the value of N.Correct answer is '6'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A wire of length L and 3 identical cells, of negligible internal resistance, are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time. Find the value of N.Correct answer is '6'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of length L and 3 identical cells, of negligible internal resistance, are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time. Find the value of N.Correct answer is '6'. Can you explain this answer?.
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A wire of length L and 3 identical cells, of negligible internal resistance, are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time. Find the value of N.Correct answer is '6'. Can you explain this answer?, a detailed solution for A wire of length L and 3 identical cells, of negligible internal resistance, are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time. Find the value of N.Correct answer is '6'. Can you explain this answer? has been provided alongside types of A wire of length L and 3 identical cells, of negligible internal resistance, are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time. Find the value of N.Correct answer is '6'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A wire of length L and 3 identical cells, of negligible internal resistance, are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time. Find the value of N.Correct answer is '6'. Can you explain this answer? tests, examples and also practice JEE tests.
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