JEE Exam > JEE Questions > A battery of unknown emf connected to a poten...
Start Learning for Free
A battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of 'n' is
Correct answer is '12'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A battery of unknown emf connected to a potentiometer has balancing le...
Let the emf of cell is e internal resistance is 'r' and potential gradient is x.
only cell connected :
ε = 560 x ................. (i)
After connecting the resistor
................... (ii)
from (1) and (2)
56 = 50 + 5r
n = 12
only cell connected :
ε = 560 x ................. (i)
After connecting the resistor
................... (ii)from (1) and (2)
56 = 50 + 5r
n = 12
Most Upvoted Answer
A battery of unknown emf connected to a potentiometer has balancing le...
To solve this problem, we can use the formula for balancing length in a potentiometer:
L = (R / (R + r)) * 100
Where L is the balancing length, R is the resistance in the potentiometer wire, and r is the internal resistance of the cell.
Let's denote the unknown emf of the battery as E and its internal resistance as n/10.
Given that the balancing length is 560 cm without any additional resistance, we have:
560 = (R / (R + n/10)) * 100
Similarly, with a resistor of resistance 10Ω connected in parallel with the cell, the balancing length changes to 500 cm. Therefore, we have:
500 = (R / (R + n/10 + 10)) * 100
Let's solve these two equations simultaneously to find the values of R and n.
First, let's simplify the equations:
560 = (R / (R + n/10)) * 100
500 = (R / (R + n/10 + 10)) * 100
Now, let's cross-multiply and simplify further:
56(R + n/10) = 10R
50(R + n/10 + 10) = 10R
Simplifying and rearranging terms:
56R + 5.6n = 10R
50R + 5n + 500 = 10R
Combining like terms:
46R = -5.6n
40R - 5n = -500
Dividing the first equation by 46 and the second equation by 5:
R = -0.122n
8R - n = -100
Substituting the value of R from the first equation into the second equation:
8(-0.122n) - n = -100
-0.976n - n = -100
-1.976n = -100
n = 50.5
Therefore, the internal resistance of the cell is 50.5/10 = 5.05Ω.
L = (R / (R + r)) * 100
Where L is the balancing length, R is the resistance in the potentiometer wire, and r is the internal resistance of the cell.
Let's denote the unknown emf of the battery as E and its internal resistance as n/10.
Given that the balancing length is 560 cm without any additional resistance, we have:
560 = (R / (R + n/10)) * 100
Similarly, with a resistor of resistance 10Ω connected in parallel with the cell, the balancing length changes to 500 cm. Therefore, we have:
500 = (R / (R + n/10 + 10)) * 100
Let's solve these two equations simultaneously to find the values of R and n.
First, let's simplify the equations:
560 = (R / (R + n/10)) * 100
500 = (R / (R + n/10 + 10)) * 100
Now, let's cross-multiply and simplify further:
56(R + n/10) = 10R
50(R + n/10 + 10) = 10R
Simplifying and rearranging terms:
56R + 5.6n = 10R
50R + 5n + 500 = 10R
Combining like terms:
46R = -5.6n
40R - 5n = -500
Dividing the first equation by 46 and the second equation by 5:
R = -0.122n
8R - n = -100
Substituting the value of R from the first equation into the second equation:
8(-0.122n) - n = -100
-0.976n - n = -100
-1.976n = -100
n = 50.5
Therefore, the internal resistance of the cell is 50.5/10 = 5.05Ω.
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
|
|
Similar JEE Doubts
Top Courses for JEEView all
A battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of n isCorrect answer is '12'. Can you explain this answer?
Question Description
A battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of n isCorrect answer is '12'. 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 battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of n isCorrect answer is '12'. 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 battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of n isCorrect answer is '12'. Can you explain this answer?.
A battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of n isCorrect answer is '12'. 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 battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of n isCorrect answer is '12'. 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 battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of n isCorrect answer is '12'. Can you explain this answer?.
Solutions for A battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of n isCorrect answer is '12'. 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 A battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of n isCorrect answer is '12'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of n isCorrect answer is '12'. Can you explain this answer?, a detailed solution for A battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of n isCorrect answer is '12'. Can you explain this answer? has been provided alongside types of A battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of n isCorrect answer is '12'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A battery of unknown emf connected to a potentiometer has balancing length 560 cm. If a resistor of resistance 10W is connected in parallel with the cell the balancing length change by 60 cm. If the internal resistance of the cell is n/10 Ω, the value of n isCorrect answer is '12'. 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup