Question

When n resistances each of value r are connected in parallel, then resultant resistance is x. When these n resistances are connected in series, total resistance is
A) nx (B) rnx (C) x / n (D) n2 x.

Answer 1

Answer would be n2x.

1/Re=1/r +1/r +1/r...n/r

1/Re= n/r (in case of parallel)

Re=r/n ----> x=r/n

r=xn

so now in case of series

it would be n2 times of resultant resistance x.

Re= r+r+.....nr

Re=nr (as r=xn)

so,

Re=n*xn

Re=n2x

Answer 2

Answer:

The total resistance is $n^{2}x$.

Explanation: When n resistance each of value r are connected in parallel, then resultant resistance is x.

Solution:

$\frac{1}{Re} =\frac{1}{r}+\frac{1}{r}+\frac{1}{r}...........\frac{n}{r}$

$\frac{1}{Re}= \frac{n}{r}$ ( in case of parallel)

$Re= \frac{r}{n}$

$x=\frac{r}{n}$

$r=xn$.

So, now in case of series.

it would be $n^{2}$ times of resultant resistance $x$.

$Re=r+r+........nr$

$Re=nr$ as $r=xn$

So,

$Re = n\times xn$

$Re = n^{2}x$

Hence, the total resistance is $n^{2}x$.

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