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An infinite ladder network is made of identical sections; each section has a series resistor of 3 Ω followed by a shunt resistor of 6 Ω. A 24 V…

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An infinite ladder network is made of identical sections; each section has a series resistor of

3\ \Omega

followed by a shunt resistor of

6\ \Omega

. A

24\ \mathrm{V}

battery is connected across the input of the ladder. The current, in amperes, flowing through the second series resistor (the one in the second section) is

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Answer: 2

Let the ladder resistance be

x

x=3+\dfrac{6x}{6+x}\Rightarrow x^2-3x-18=0\Rightarrow x=6\ \Omega

. Input current

=24/6=4\ \mathrm{A}

. Drop across the first series resistor

=12\ \mathrm{V}

, leaving

12\ \mathrm{V}

across the first shunt and across the remaining ladder (which again has resistance

6\ \Omega

). The current into the second section, i.e. through the second series resistor, is

12/6=2\ \mathrm{A}

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