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Two coils connected in series have a resistance of 18 ohm and when connected in parallel have a resistance of 4 ohm. Find the value of individual resistance of the coils.?
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Two coils connected in series have a resistance of 18 ohm and when con...
Explanation:
Let's assume that the resistance of the first coil is R1 and the resistance of the second coil is R2.
When two coils are connected in series, the total resistance is the sum of individual resistances. Therefore,
Total resistance in series = R1 + R2 = 18 ohm
When the same two coils are connected in parallel, the total resistance is given by the formula:
Total resistance in parallel = (R1 x R2) / (R1 + R2) = 4 ohm
Solving for R1 and R2:
We can use simultaneous equations to find the values of R1 and R2.
From the first equation, we get:
R1 + R2 = 18
R2 = 18 - R1
Substituting this value into the second equation, we get:
(R1 x (18 - R1)) / (R1 + (18 - R1)) = 4
R1 x (18 - R1) / 18 = 4
Multiplying both sides by 18, we get:
R1 x (18 - R1) = 72
Expanding the brackets, we get:
18R1 - R1^2 = 72
R1^2 - 18R1 + 72 = 0
Solving this quadratic equation, we get:
R1 = 12 ohm or R1 = 6 ohm
If R1 = 12 ohm, then R2 = 6 ohm (from R2 = 18 - R1)
If R1 = 6 ohm, then R2 = 12 ohm (from R2 = 18 - R1)
Therefore, the individual resistance of the two coils are 12 ohm and 6 ohm.
Conclusion:
When two coils are connected in series, their resistances add up. When the same two coils are connected in parallel, their resistances are inversely proportional to their individual resistances. Using these formulas, we can solve for the values of individual resistances of the coils.
Let's assume that the resistance of the first coil is R1 and the resistance of the second coil is R2.
When two coils are connected in series, the total resistance is the sum of individual resistances. Therefore,
Total resistance in series = R1 + R2 = 18 ohm
When the same two coils are connected in parallel, the total resistance is given by the formula:
Total resistance in parallel = (R1 x R2) / (R1 + R2) = 4 ohm
Solving for R1 and R2:
We can use simultaneous equations to find the values of R1 and R2.
From the first equation, we get:
R1 + R2 = 18
R2 = 18 - R1
Substituting this value into the second equation, we get:
(R1 x (18 - R1)) / (R1 + (18 - R1)) = 4
R1 x (18 - R1) / 18 = 4
Multiplying both sides by 18, we get:
R1 x (18 - R1) = 72
Expanding the brackets, we get:
18R1 - R1^2 = 72
R1^2 - 18R1 + 72 = 0
Solving this quadratic equation, we get:
R1 = 12 ohm or R1 = 6 ohm
If R1 = 12 ohm, then R2 = 6 ohm (from R2 = 18 - R1)
If R1 = 6 ohm, then R2 = 12 ohm (from R2 = 18 - R1)
Therefore, the individual resistance of the two coils are 12 ohm and 6 ohm.
Conclusion:
When two coils are connected in series, their resistances add up. When the same two coils are connected in parallel, their resistances are inversely proportional to their individual resistances. Using these formulas, we can solve for the values of individual resistances of the coils.
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Two coils connected in series have a resistance of 18 ohm and when connected in parallel have a resistance of 4 ohm. Find the value of individual resistance of the coils.?
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Two coils connected in series have a resistance of 18 ohm and when connected in parallel have a resistance of 4 ohm. Find the value of individual resistance of the coils.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two coils connected in series have a resistance of 18 ohm and when connected in parallel have a resistance of 4 ohm. Find the value of individual resistance of the coils.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two coils connected in series have a resistance of 18 ohm and when connected in parallel have a resistance of 4 ohm. Find the value of individual resistance of the coils.?.
Two coils connected in series have a resistance of 18 ohm and when connected in parallel have a resistance of 4 ohm. Find the value of individual resistance of the coils.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two coils connected in series have a resistance of 18 ohm and when connected in parallel have a resistance of 4 ohm. Find the value of individual resistance of the coils.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two coils connected in series have a resistance of 18 ohm and when connected in parallel have a resistance of 4 ohm. Find the value of individual resistance of the coils.?.
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