Question

a wire of resistance r is cut into five equal peices. these pieces are connected in parallel and the equivalent resistance are rn. find the ratio of r/rn

Answer 1

I hope u are getting my handwritting if not then please tell me

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

$\tt Given \begin{cases} \sf{Wire \: is \: cutted \: into \: 5 \: equal \: parts} \\ \sf{Resistance \: of \: wire \: is \: R} \end{cases}$

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To Find :

$\hookrightarrow \sf{ratio \: of \: \frac{r}{r_{n} } }$

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Solution :

Resistance of price of length L/5 = R/5

So,

The equivalent resistance of the 5 wires in parallel is Rn. Then,

We know Formula of resistance in parallel

$\Large \implies {\boxed{\boxed{\sf{\frac{1}{R_{n}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} ......... \frac{1}{R'} }}}}$

(Putting Values)

$\sf{\rightarrow \frac{1}{R_n} = \frac{ \frac{1}{R} }{5} + \frac{ \frac{1}{R} }{5} + \frac{ \frac{1}{R} }{5} + \frac{ \frac{1}{R} }{5} + \frac{ \frac{1}{R} }{5} + } \\ \\ \sf{\rightarrow \frac{1}{R_n} = \frac{5}{R_n} + \frac{5}{R_n} + \frac{5}{R_n} + \frac{5}{R_n} + \frac{5}{R_n} } \\ \\ \sf{{\rightarrow \frac{1}{R_n} = \frac{5 + 5 + 5 + 5 + 5}{R} } } \\ \\ \sf{\rightarrow \frac{1}{R_n} = \frac{25}{R} } \\ \\ \sf{\rightarrow \frac{R}{R_n} = \frac{25}{1} } \\ \\ \Large{\leadsto {\underline{\boxed{\sf{R : R_n = 25 : 1}}}}}$

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