Question

lobh - lobh(100)

⚡A set of n indentical resistors, each od resistance R ohm, when connected in series have an effective resistance X ohm and when connected in parallel, their effective resistance is Y ohm. find relation between X and Y. ​

Answer 1

Hello Dear Friend ❤

⏬Answer⏬

In series

nR = X

In parellel

R/n = Y

Ratio of X and Y = nR / (R/n) = n²

X : Y = n² : 1

__________________

Given,

Their is a set of n resistors.

each resistor is of resistance R ohm.

Conditions :

When they are connected in Series,

the equivalent is Xohm.

X = R + R+ R+ ... n terms = nR

X = nR

When they are connected in Parallel combination,

the equivalent is Y ohm.

1/Y = 1/R + 1/R + 1/R .... n terms = n/R

or Y = R/n

On multiplying X and Y we get,

XY = R×R

XY = R^{2}R

2

R = √XY

___________________

✌Hope it helps✌

✔✔ Be Brainly ✔✔

Answer 2

Given,

Their is a  set of n resistors.

each resistor is of resistance R ohm.

Conditions :

When they are connected in Series,

the equivalent is Xohm.

X = R + R+ R+ ... n terms = nR

X = nR

When they are connected in Parallel combination,

the equivalent is Y ohm.

1/Y = 1/R + 1/R + 1/R

.... n terms = n/R

or  Y = R/n

On multiplying X and Y we get,

XY = R×R

XY = $R^{2}$

$R = \sqrt[]{XY}$

∴Relation between X and Y is $\sqrt[]{XY}$