Question

there are m resistors each of resistance R. First they all are connected in series and equivallent resistance is X.Now they are conneced in parallel and equivalent resistance is y What is the ratio of X and Y

Answer 1

m square......................

Answer 2

Aɴꜱᴡᴇʀ

$\huge{\sf{x : y = m^2 : 1}}$

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Gɪᴠᴇɴ

• m resistors of resistance R are first connected in series and then connected in parallel.

• resistance of series connection = x

• resistance of parallel connection = y

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ᴛᴏ ꜰɪɴᴅ

The ratio between X and Y

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Sᴛᴇᴘꜱ

Here we can use the formula

$\boxed{ \fbox{\sf{\red{R_{eq}=R_1+R_2+R_3+.....}}}}$

Formula of equation resistance in parallel connection is given by >>

$\boxed{ \fbox{\sf{\pink{\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+.....}}}}$

Series Connection

$\begin{lgathered}\dashrightarrow\sf\:R_{s}=R+R+..... m \:times\\ \\ \dashrightarrow\:{\sf{\orange{\large{x=mR}}}}\end{lgathered}$

Parallel Connection

$\begin{lgathered}\leadsto\sf\:\dfrac{1}{R_p}=\dfrac{1}{R}+\dfrac{1}{R}+.....m \: times\\ \\ \dashrightarrow\sf\:\dfrac{1}{y}=\dfrac{m}{R}\\ \\ \dashrightarrow\:{\sf{\orange{\large{y=\dfrac{R}{m}}}}}\end{lgathered}$

Ratio of X and Y is

$\begin{lgathered}\mapsto\sf\:\dfrac{x}{y}=\dfrac{mR}{\frac{R}{m}}\\ \\ \mapsto\:\boxed{ \fbox{\tt{\pink{\large{x : y = m^2 : 1}}}}}\end{lgathered}</p><p>$

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$\huge{\mathfrak{\purple{hope\; it \;helps}}}$