JEE Exam > JEE Questions > If a cell of constant electromotive force pro...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
If a cell of constant electromotive force produces the same amount of ...
(R + R)/2
d)(2R)/(R+R)
Answer:
c) (R + R)/2
Explanation:
Let the internal resistance of the cell be r.
When one resistance R is connected, the current flowing through it is I1 = E/(R+r).
The heat produced in time t is Q1 = I1^2Rt = E^2Rt/(R+r)^2.
When the other resistance R is connected, the current flowing through it is I2 = E/(R+r).
The heat produced in time t is Q2 = I2^2Rt = E^2Rt/(R+r)^2.
Since the amount of heat produced is the same in both cases, we have Q1 = Q2.
Therefore, E^2Rt/(R+r)^2 = E^2Rt/(R+r)^2.
Simplifying this, we get R = R.
Hence, the internal resistance of the cell is (R + R)/2.
d)(2R)/(R+R)
Answer:
c) (R + R)/2
Explanation:
Let the internal resistance of the cell be r.
When one resistance R is connected, the current flowing through it is I1 = E/(R+r).
The heat produced in time t is Q1 = I1^2Rt = E^2Rt/(R+r)^2.
When the other resistance R is connected, the current flowing through it is I2 = E/(R+r).
The heat produced in time t is Q2 = I2^2Rt = E^2Rt/(R+r)^2.
Since the amount of heat produced is the same in both cases, we have Q1 = Q2.
Therefore, E^2Rt/(R+r)^2 = E^2Rt/(R+r)^2.
Simplifying this, we get R = R.
Hence, the internal resistance of the cell is (R + R)/2.
Free Test
FREE
| Start Free Test |
Community Answer
If a cell of constant electromotive force produces the same amount of ...
(R + R)/2
d)(2R)/(R + R)
e)None of the above
We can use the formula for heat produced in a resistor:
H = I^2Rt
where I is the current, R is the resistance, and t is the time. Since the cell has a constant electromotive force, the current will be the same in both cases. Let's call the current I.
When the first resistance R is connected, the heat produced is:
H1 = I^2Rt
When the second resistance R is connected, the heat produced is:
H2 = I^2Rt
Since the amount of heat produced is the same in both cases, we can set H1 equal to H2 and solve for the internal resistance of the cell.
I^2Rt = I^2Rt
Rt = R + r + R
where r is the internal resistance of the cell. We can simplify this equation:
2Rt = 2R + r*t
r = 2Rt - 2R/t
r = 2R - 2R/t
r = (2R)/(1/t)
r = (2R)t
We don't know the value of t, but we do know that it is the same in both cases. So, we can say that t cancels out and the internal resistance of the cell is:
r = 2R
Therefore, the answer is (e) None of the above.
d)(2R)/(R + R)
e)None of the above
We can use the formula for heat produced in a resistor:
H = I^2Rt
where I is the current, R is the resistance, and t is the time. Since the cell has a constant electromotive force, the current will be the same in both cases. Let's call the current I.
When the first resistance R is connected, the heat produced is:
H1 = I^2Rt
When the second resistance R is connected, the heat produced is:
H2 = I^2Rt
Since the amount of heat produced is the same in both cases, we can set H1 equal to H2 and solve for the internal resistance of the cell.
I^2Rt = I^2Rt
Rt = R + r + R
where r is the internal resistance of the cell. We can simplify this equation:
2Rt = 2R + r*t
r = 2Rt - 2R/t
r = 2R - 2R/t
r = (2R)/(1/t)
r = (2R)t
We don't know the value of t, but we do know that it is the same in both cases. So, we can say that t cancels out and the internal resistance of the cell is:
r = 2R
Therefore, the answer is (e) None of the above.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
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?.
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?.
Solutions 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? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup