Question

There are m resistor each of resistance R. First, they all are connected in series and equivalent resistance is x. Now they are connected in parallel and equivalent resistance is Y. What is the ratio of X and Y?

Answer 1

Given 

Number of the Resistors = m
Resistance in each Resistor = R

When they are connected in series,
Equivalent Resistance = R + R + R +R +........ m times.
 X = R × m
 ∴ X = Rm.


Now, When they are connected in Parallel,

1/Req. = 1/R + 1/R + 1/R + 1/R +........ m times.
 1/Req.= m/R
∴ Y = R/m

Now Ratio of X an Y is ⇒

X/Y = Rm/(R/m)
= Rm²/R
= m²/1


Hence, the ratio of the X and Y is m² :1.


Hope it helps.

Answer 2

i hope its HELPFUL.

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