JEE Exam > JEE Questions > Three unequal resistors in parallel are equiv...
Start Learning for Free
Three unequal resistors in parallel are equivalent to resistance 1 Ω . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms is
- a)4
- b)6
- c)8
- d)12
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Three unequal resistors in parallel are equivalent to resistance 1 . ...
To solve this problem, let's assign variables to the resistances. Let the resistances be R1, R2, and R3.
According to the problem, R1, R2, and R3 are connected in parallel and their equivalent resistance is 1 ohm.
Using the formula for the equivalent resistance of resistors in parallel, we have:
1/R = 1/R1 + 1/R2 + 1/R3
Since the resistances are unequal, we can write R2 = 2R1 and R3 = kR1, where k is a constant.
Substituting these values into the equation above, we get:
1/R = 1/R1 + 1/(2R1) + 1/(kR1)
To simplify the equation, we can find a common denominator:
1/R = (2 + 1/k) / (2R1)
Now, we can equate the numerator of the right side of the equation to 1, since the equivalent resistance is given as 1 ohm:
2 + 1/k = 1
Simplifying the equation, we have:
2 + 1/k = 1
Subtracting 2 from both sides, we get:
1/k = -1
Taking the reciprocal of both sides, we have:
k = -1
Since resistance values cannot be negative, we can discard the negative solution. Therefore, k = -1 is not valid.
Now, let's substitute k = 1 into the equation:
1/R = (2 + 1/1) / (2R1)
Simplifying further, we have:
1/R = 3 / (2R1)
Multiplying both sides by 2R1, we get:
2R1 / R = 3
Simplifying the left side of the equation, we have:
2 = 3
This is not a valid solution.
Therefore, the only valid solution is k = 1, which means R3 = R1.
Since the resistances are in the ratio 1:2, R1:R2:R3 = 1:2:2.
Since we know that the sum of the resistances is 1 ohm, we can write:
R1 + R2 + R3 = 1
Substituting the values, we have:
R1 + 2R1 + 2R1 = 1
Simplifying the equation, we get:
5R1 = 1
Dividing both sides by 5, we find:
R1 = 1/5 = 0.2 ohms
Since the largest resistance is R3, we can conclude that R3 = 2R1 = 2(0.2) = 0.4 ohms.
Therefore, the largest of the three resistances is 0.4 ohms, which corresponds to option B.
According to the problem, R1, R2, and R3 are connected in parallel and their equivalent resistance is 1 ohm.
Using the formula for the equivalent resistance of resistors in parallel, we have:
1/R = 1/R1 + 1/R2 + 1/R3
Since the resistances are unequal, we can write R2 = 2R1 and R3 = kR1, where k is a constant.
Substituting these values into the equation above, we get:
1/R = 1/R1 + 1/(2R1) + 1/(kR1)
To simplify the equation, we can find a common denominator:
1/R = (2 + 1/k) / (2R1)
Now, we can equate the numerator of the right side of the equation to 1, since the equivalent resistance is given as 1 ohm:
2 + 1/k = 1
Simplifying the equation, we have:
2 + 1/k = 1
Subtracting 2 from both sides, we get:
1/k = -1
Taking the reciprocal of both sides, we have:
k = -1
Since resistance values cannot be negative, we can discard the negative solution. Therefore, k = -1 is not valid.
Now, let's substitute k = 1 into the equation:
1/R = (2 + 1/1) / (2R1)
Simplifying further, we have:
1/R = 3 / (2R1)
Multiplying both sides by 2R1, we get:
2R1 / R = 3
Simplifying the left side of the equation, we have:
2 = 3
This is not a valid solution.
Therefore, the only valid solution is k = 1, which means R3 = R1.
Since the resistances are in the ratio 1:2, R1:R2:R3 = 1:2:2.
Since we know that the sum of the resistances is 1 ohm, we can write:
R1 + R2 + R3 = 1
Substituting the values, we have:
R1 + 2R1 + 2R1 = 1
Simplifying the equation, we get:
5R1 = 1
Dividing both sides by 5, we find:
R1 = 1/5 = 0.2 ohms
Since the largest resistance is R3, we can conclude that R3 = 2R1 = 2(0.2) = 0.4 ohms.
Therefore, the largest of the three resistances is 0.4 ohms, which corresponds to option B.
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
Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. Can you explain this answer?
Question Description
Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. 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 Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. Can you explain this answer?.
Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. 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 Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. Can you explain this answer?.
Solutions for Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. 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 Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. 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