An infinite ladder network is made of…

An infinite ladder network is made of identical repeating sections, each having a 1 Ω resistor in series along the top rail followed by a 2 Ω…

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An infinite ladder network is made of identical repeating sections, each having a

1\ \Omega

resistor in series along the top rail followed by a

2\ \Omega

resistor connected across the two rails. A battery of emf

12\ \mathrm{V}

and negligible internal resistance is connected to the input end. The current through the first

2\ \Omega

cross resistor is

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Answer: (A) $3\ \mathrm{A}$

Let the resistance of the whole infinite ladder be

x

. Removing the first section leaves an identical ladder, so

x = 1 + \dfrac{2x}{2+x}

, which gives

x^2 - x - 2 = 0

and

x = 2\ \Omega

. The battery current is

12/2 = 6\ \mathrm{A}

. The voltage across the first cross resistor is

12 - 6\times1 = 6\ \mathrm{V}

, so the current in it is

6/2 = 3\ \mathrm{A}

. Check: the rest of the ladder is also

2\ \Omega

6\ \mathrm{V}

, taking

3\ \mathrm{A}

, and

3 + 3 = 6\ \mathrm{A}

. The value

6\ \mathrm{A}

is the total current.

Original question written in the JEE Main 2017 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake