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If a cell of constant electromotive force produces the same amount of heat during the same time in two independent resistances R₁ and R₂, when connected separately one after the other, across the cell, then the internal resistance of the cell is
  • a)
    (R₁ + R₂)
  • b)
    (R₁ - R₂)/2
  • c)
    √R₁ R₂/2
  • d)
    √R₁ R₂
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If a cell of constant electromotive force produces the same amount of ...
Concept:
When a cell of constant electromotive force produces the same amount of heat during the same time in two independent resistances R and R, connected separately one after the other, across the cell, then the internal resistance of the cell can be determined using the concept of equivalent resistance.

Solution:

Given:
- Two resistances R and R connected separately one after the other across the cell.
- The heat produced in both resistances is the same.

Analysis:
When the resistances are connected one after the other, the total heat produced in the resistances is the same. Let the total heat produced be Q.
Let the internal resistance of the cell be 'r'.

Calculations:
When resistance R is connected:
- Heat produced = I^2 * R * t
- Voltage across the resistance R = V = EMF - IR
- Current through resistance R = I = V / R = (EMF - IR) / R
- Heat produced in resistance R = [(EMF - IR) / R]^2 * R * t = (EMF - Ir)^2 * t / R
When resistance R is connected:
- Heat produced = I^2 * R * t
- Voltage across the resistance R = V = EMF - IR
- Current through resistance R = I = V / R = (EMF - IR) / R
- Heat produced in resistance R = [(EMF - IR) / R]^2 * R * t = (EMF - Ir)^2 * t / R
Since the total heat produced is the same in both cases:
- (EMF - Ir)^2 * t / R = (EMF - Ir)^2 * t / R
- r = √(R * R) = √(R^2) = R
Therefore, the internal resistance of the cell is √(R * R) = R.
Therefore, the correct answer is option 'D'.
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If a cell of constant electromotive force produces the same amount of heat during the same time in two independent resistances R and R, when connected separately one after the other, across the cell, then the internal resistance of the cell isa)(R + R)b)(R - R)/2c)√R R/2d)√R RCorrect answer is option 'D'. Can you explain this answer?
Question Description
If a cell of constant electromotive force produces the same amount of heat during the same time in two independent resistances R and R, when connected separately one after the other, across the cell, then the internal resistance of the cell isa)(R + R)b)(R - R)/2c)√R R/2d)√R RCorrect answer is option 'D'. 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 If a cell of constant electromotive force produces the same amount of heat during the same time in two independent resistances R and R, when connected separately one after the other, across the cell, then the internal resistance of the cell isa)(R + R)b)(R - R)/2c)√R R/2d)√R RCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a cell of constant electromotive force produces the same amount of heat during the same time in two independent resistances R and R, when connected separately one after the other, across the cell, then the internal resistance of the cell isa)(R + R)b)(R - R)/2c)√R R/2d)√R RCorrect answer is option 'D'. Can you explain this answer?.
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