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?

Question

Answer

When connected in series
x=mr
when in parallel
y=r/m
x/y=mr/r/m=m×m

Answer

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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