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There are m resistors each of resistance r first they all are connected in series and equivalent resistance is it now they are connected in parallel and equivalent resistance is why what is the ratio of x and y?
Most Upvoted Answer
There are m resistors each of resistance r first they all are connecte...
When connected in series
x=mr
when in parallel
y=r/m
x/y=mr/r/m=m×m
x=mr
when in parallel
y=r/m
x/y=mr/r/m=m×m
Community Answer
There are m resistors each of resistance r first they all are connecte...
Explanation of the problem
In this problem, we are given that there are m resistors each of resistance r. We are first asked to connect them in series and find the equivalent resistance. Then we are asked to connect them in parallel and find the equivalent resistance. Finally, we are asked to find the ratio of the two equivalent resistances.
Connecting resistors in series
When resistors are connected in series, their resistances add up. So, if we have m resistors each of resistance r, their equivalent resistance when connected in series would be:
Rs = mr
Connecting resistors in parallel
When resistors are connected in parallel, their equivalent resistance is given by the formula:
Rp = r/n
where n is the number of resistors connected in parallel.
In our case, we have m resistors connected in parallel, so their equivalent resistance would be:
Rp = r/m
Ratio of equivalent resistances
Now, we need to find the ratio of Rp to Rs:
Rp/Rs = (r/m)/(mr) = 1/m^2
So, the ratio of Rp to Rs is 1/m^2.
Conclusion
In this problem, we have learned how to find the equivalent resistance of resistors when they are connected in series and in parallel. We have also found the ratio of the two equivalent resistances.
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There are m resistors each of resistance r first they all are connected in series and equivalent resistance is it now they are connected in parallel and equivalent resistance is why what is the ratio of x and y?
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There are m resistors each of resistance r first they all are connected in series and equivalent resistance is it now they are connected in parallel and equivalent resistance is why what is the ratio of x and y? 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 There are m resistors each of resistance r first they all are connected in series and equivalent resistance is it now they are connected in parallel and equivalent resistance is why what is the ratio of x and y? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are m resistors each of resistance r first they all are connected in series and equivalent resistance is it now they are connected in parallel and equivalent resistance is why what is the ratio of x and y?.
There are m resistors each of resistance r first they all are connected in series and equivalent resistance is it now they are connected in parallel and equivalent resistance is why what is the ratio of x and y? 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 There are m resistors each of resistance r first they all are connected in series and equivalent resistance is it now they are connected in parallel and equivalent resistance is why what is the ratio of x and y? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are m resistors each of resistance r first they all are connected in series and equivalent resistance is it now they are connected in parallel and equivalent resistance is why what is the ratio of x and y?.
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