Question 604: Current Electricity

Question

The equivalent resistance of the infinite network given below is :
![](https://app-content.cdn.examgoal.net/fly/@width/image/1lab19sk5/c2c97eb6-1190-48ac-b61b-fb6ea9e2645b/605d1050-60f1-11ed-b81b-f1e44e9e12b2/file-1lab19sk6.png?format=png)

Accepted Answer

Let net resistance of the given infinite network be 'R'
Now, the circuit can be modified as
Now, ${R_{net}} = R = 1 + 1 + {R \over {R + 1}}$
$	herefore$ $R = 2 + {R \over {R + 1}}$
${R^2} + R = 2R + 2 + R$
${R^2} - 2R - 2 = 0$
$R = \left( {{{2\, \pm \,\sqrt {4 + 8} } \over 2}} ight)$
$R = \left( {1 + \sqrt 3 } ight)\Omega $
![](https://app-content.cdn.examgoal.net/fly/@width/image/1lab1am4d/06986e80-bdeb-4c3c-b487-644bde3ae7df/773302d0-60f1-11ed-b81b-f1e44e9e12b2/file-1lab1am4e.png?format=png)

Answer

$\left( {1 + \sqrt 5 } \right)\Omega $

Answer

$2\,\Omega $

Answer

$\left( {1 + \sqrt 2 } \right)\Omega $

Answer

$\left( {1 + \sqrt 3 } \right)\Omega $

Current Electricity

The equivalent resistance of the infinite network given below is :

Choose the correct answer: