An infinite ladder network of resistances is constructed with 1 Ω and 2 Ω resistances. The 6 V battery has negligible internal resistance. The current that passes through the 2 Ω resistance nearest to the battery is

Question

An infinite ladder network of resistances is constructed with 1 Ω and 2 Ω resistances. The 6 V battery has negligible internal resistance. The current that passes through the 2 Ω resistance nearest to the battery is, 1 A, 1.5 A, 2 A, 2.5 A

MARKS App · Accepted Answer

Let x be the equivalent resistance of the infinite ladder then, the equivalent circuit is also, the equivalent resistance is x = 1 + 2 x 2 + x x 2 - x - 2 = 0 x = 1 + 1 + 8 2 = 2 Ω current through the battery is 3 A . Current through 2 Ω resistor is i = 3 x 2 + x = 3 2 2 + 2 = 1.5 A

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