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Current Electricity question

2022 · Q160
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Current Electricity question

2022 · Q160

NEETPhysicsCurrent ElectricityMCQ+4 / −1

The equivalent resistance of the infinite network given below is :

NEET 2022 Phase 2 Physics - Current Electricity Question 21 English

  1. A
    (1+5)Ω\left( {1 + \sqrt 5 } \right)\Omega(1+5​)Ω
  2. B
    2 Ω2\,\Omega2Ω
  3. C
    (1+2)Ω\left( {1 + \sqrt 2 } \right)\Omega(1+2​)Ω
  4. D
    (1+3)Ω\left( {1 + \sqrt 3 } \right)\Omega(1+3​)Ω
View written solutionFree

Correct answer: D

Let net resistance of the given infinite network be 'R'

Now, the circuit can be modified as

NEET 2022 Phase 2 Physics - Current Electricity Question 21 English Explanation

Now, $${R_{net}} = R = 1 + 1 + {R \over {R + 1}}$$

$\therefore$ $$R = 2 + {R \over {R + 1}}$$

$${R^2} + R = 2R + 2 + R$$

${R^2} - 2R - 2 = 0$

$$R = \left( {{{2\, \pm \,\sqrt {4 + 8} } \over 2}} \right)$$

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

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