JEE Exam > JEE Questions > Three unequal resistors in parallel are equiv...
Start Learning for Free
Three unequal resistors in parallel are equivalent to a resistance 1 ohm. 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 a resistance 1 o...
To solve this problem, we can use the concept of equivalent resistance in parallel circuits. Let's break down the problem step by step.
Let the three resistors be R₁, R₂, and R₃, with R₁ having the smallest resistance, R₂ having twice the resistance of R₁, and R₃ having the largest resistance.
Step 1: Write the equations for the equivalent resistance in parallel.
The formula for calculating the equivalent resistance in parallel is:
1/Req = 1/R₁ + 1/R₂ + 1/R₃
Step 2: Substitute the given information into the equation.
Since the equivalent resistance is given as 1 ohm, we can rewrite the equation as:
1 = 1/R₁ + 1/R₂ + 1/R₃
Since R₁ and R₂ are in a 1:2 ratio, we can express R₂ in terms of R₁:
R₂ = 2R₁
Step 3: Substitute the expression for R₂ into the equation.
1 = 1/R₁ + 1/(2R₁) + 1/R₃
Step 4: Simplify the equation.
To simplify the equation, we can find a common denominator and combine the fractions:
1 = (2 + 1)/(2R₁) + 1/R₃
1 = 3/(2R₁) + 1/R₃
1 = (3R₃ + 2R₁)/(2R₁R₃)
Step 5: Determine the possible values for R₁ and R₃.
Since no resistance value is fractional, R₁ and R₃ must be integers. We can start by assuming R₁ = 1 and find the corresponding value of R₃.
1 = (3R₃ + 2)/(2R₃)
2R₃ = 3R₃ + 2
R₃ = 2
However, this solution does not satisfy the condition that R₃ is the largest resistance. Let's try assuming R₁ = 2 instead and find the corresponding value of R₃.
1 = (3R₃ + 4)/(4R₃)
4R₃ = 3R₃ + 4
R₃ = 4
Now, we have a valid solution where R₁ = 2 and R₃ = 4. We can find the value of R₂ by using the given ratio:
R₂ = 2R₁
R₂ = 2(2)
R₂ = 4
Therefore, the largest of the three resistances is R₃ = 4 ohms.
Hence, the correct answer is option B) 6.
Let the three resistors be R₁, R₂, and R₃, with R₁ having the smallest resistance, R₂ having twice the resistance of R₁, and R₃ having the largest resistance.
Step 1: Write the equations for the equivalent resistance in parallel.
The formula for calculating the equivalent resistance in parallel is:
1/Req = 1/R₁ + 1/R₂ + 1/R₃
Step 2: Substitute the given information into the equation.
Since the equivalent resistance is given as 1 ohm, we can rewrite the equation as:
1 = 1/R₁ + 1/R₂ + 1/R₃
Since R₁ and R₂ are in a 1:2 ratio, we can express R₂ in terms of R₁:
R₂ = 2R₁
Step 3: Substitute the expression for R₂ into the equation.
1 = 1/R₁ + 1/(2R₁) + 1/R₃
Step 4: Simplify the equation.
To simplify the equation, we can find a common denominator and combine the fractions:
1 = (2 + 1)/(2R₁) + 1/R₃
1 = 3/(2R₁) + 1/R₃
1 = (3R₃ + 2R₁)/(2R₁R₃)
Step 5: Determine the possible values for R₁ and R₃.
Since no resistance value is fractional, R₁ and R₃ must be integers. We can start by assuming R₁ = 1 and find the corresponding value of R₃.
1 = (3R₃ + 2)/(2R₃)
2R₃ = 3R₃ + 2
R₃ = 2
However, this solution does not satisfy the condition that R₃ is the largest resistance. Let's try assuming R₁ = 2 instead and find the corresponding value of R₃.
1 = (3R₃ + 4)/(4R₃)
4R₃ = 3R₃ + 4
R₃ = 4
Now, we have a valid solution where R₁ = 2 and R₃ = 4. We can find the value of R₂ by using the given ratio:
R₂ = 2R₁
R₂ = 2(2)
R₂ = 4
Therefore, the largest of the three resistances is R₃ = 4 ohms.
Hence, the correct answer is option B) 6.
Free Test
FREE
| Start Free Test |
Community Answer
Three unequal resistors in parallel are equivalent to a resistance 1 o...
Given:
- Three unequal resistors in parallel are equivalent to a resistance of 1 ohm.
- Two of the resistors are in the ratio 1:2.
- No resistance value is fractional.
To find:
The largest resistance among the three.
Solution:
Let's assume the resistors are R1, R2, and R3.
Step 1: Expressing the given information
- The resistance of resistors in parallel is given by the formula: 1/R_eq = 1/R1 + 1/R2 + 1/R3
- We are given that R1 and R2 are in the ratio 1:2, so we can express R1 and R2 as R and 2R respectively.
- Substituting R1 = R and R2 = 2R, the equation becomes: 1/R_eq = 1/R + 1/(2R) + 1/R3
Step 2: Simplifying the equation
- Combining the fractions, the equation becomes: 1/R_eq = (2 + 1)/(2R) + 1/R3
- To add the fractions, we need a common denominator, which is 2R.
- Multiplying the numerator and denominator of the first fraction by R, we get: 1/R_eq = (3R + 2)/(2R^2) + 1/R3
Step 3: Finding a relationship between R and R3
- Since no resistance value is fractional, R and R3 must be integers.
- To make the right side of the equation an integer, the denominator 2R^2 must divide R3.
- This implies that R^2 must divide R3.
Step 4: Finding the possible values of R and R3
- R and R3 are positive integers, and R^2 must divide R3.
- The possible values for R and R3 are:
- R = 1, R3 = 1
- R = 1, R3 = 2
- R = 1, R3 = 3
- R = 2, R3 = 2
- R = 2, R3 = 4
- R = 2, R3 = 6
- R = 3, R3 = 3
- R = 3, R3 = 6
- R = 4, R3 = 4
- R = 4, R3 = 8
- R = 6, R3 = 6
- R = 8, R3 = 8
Step 5: Finding the largest resistance
- From the possible values, we see that the maximum value of R3 is 8.
- Therefore, the largest resistance among the three is 8 ohms.
Answer:
The largest of the three resistances is 8 ohms, which corresponds to option B.
- Three unequal resistors in parallel are equivalent to a resistance of 1 ohm.
- Two of the resistors are in the ratio 1:2.
- No resistance value is fractional.
To find:
The largest resistance among the three.
Solution:
Let's assume the resistors are R1, R2, and R3.
Step 1: Expressing the given information
- The resistance of resistors in parallel is given by the formula: 1/R_eq = 1/R1 + 1/R2 + 1/R3
- We are given that R1 and R2 are in the ratio 1:2, so we can express R1 and R2 as R and 2R respectively.
- Substituting R1 = R and R2 = 2R, the equation becomes: 1/R_eq = 1/R + 1/(2R) + 1/R3
Step 2: Simplifying the equation
- Combining the fractions, the equation becomes: 1/R_eq = (2 + 1)/(2R) + 1/R3
- To add the fractions, we need a common denominator, which is 2R.
- Multiplying the numerator and denominator of the first fraction by R, we get: 1/R_eq = (3R + 2)/(2R^2) + 1/R3
Step 3: Finding a relationship between R and R3
- Since no resistance value is fractional, R and R3 must be integers.
- To make the right side of the equation an integer, the denominator 2R^2 must divide R3.
- This implies that R^2 must divide R3.
Step 4: Finding the possible values of R and R3
- R and R3 are positive integers, and R^2 must divide R3.
- The possible values for R and R3 are:
- R = 1, R3 = 1
- R = 1, R3 = 2
- R = 1, R3 = 3
- R = 2, R3 = 2
- R = 2, R3 = 4
- R = 2, R3 = 6
- R = 3, R3 = 3
- R = 3, R3 = 6
- R = 4, R3 = 4
- R = 4, R3 = 8
- R = 6, R3 = 6
- R = 8, R3 = 8
Step 5: Finding the largest resistance
- From the possible values, we see that the maximum value of R3 is 8.
- Therefore, the largest resistance among the three is 8 ohms.
Answer:
The largest of the three resistances is 8 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 a resistance 1 ohm. 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 a resistance 1 ohm. 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 a resistance 1 ohm. 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 a resistance 1 ohm. 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 a resistance 1 ohm. 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 a resistance 1 ohm. 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 a resistance 1 ohm. 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 a resistance 1 ohm. 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 a resistance 1 ohm. 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 a resistance 1 ohm. 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 a resistance 1 ohm. 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 a resistance 1 ohm. 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 a resistance 1 ohm. 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
|
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