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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?
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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.
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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.
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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?
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