Question

For following circuit, what is the value of total resistance between X and Y?​

Answer 1

The total resistance between X and Y is 2R.

Explanation:

Given that,

Resistance = R

According to figure,

R ₁ and R₅ connected in parallel

We need to calculate the equivalent resistance

Using formula for parallel

$\dfrac{1}{R'}=\dfrac{1}{R_{1}}+\dfrac{1}{R_{5}}$

Put the value into the formula

$\dfrac{1}{R'}=\dfrac{1}{R}+\dfrac{1}{R}$

$\dfrac{1}{R'}=\dfrac{2}{R}$

$R'=\dfrac{R}{2}$

Similarly,

(R₂, R₆), ( R₃,R₇) and (R₄,R₈) are connected in parallel

So, $R''=\dfrac{R}{2}$

$R'''=\dfrac{R}{2}$

$R''''=\dfrac{R}{2}$

Now, R', R'', R''' and R'''' are connect in series

We need to calculate the total resistance between X and Y

Using formula for series

$R_{eq}=R'+R''+R'''+R''''$

Put the value into the formula

$R_{eq}=\dfrac{R}{2}+\dfrac{R}{2}+\dfrac{R}{2}+\dfrac{R}{2}$

$R_{eq}=\dfrac{4R}{2}$

$R_{eq}=2R$

Hence, The total resistance between X and Y is 2R.

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Topic : resistance

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