Concepts/Formula used:
Resistors in Series: Resistors in parallel: Ohm’s Law:

Potential Difference (V) across a resistor of resistance R when current I passes through it is given by Ohm’s law: (a)

Let the equivalent resistance between A and B be req Ω .

This means that we can rewrite the circuit as: Where req has replaced the following infinite combination: We can redraw the infinite circuit as Note that de and cb are in parallel. The equivalent resistance is given by:   Now, the 1 Ω resistor and r’eq are in series.  Rearranging and dropping the subscript, we get a quadratic equation: The roots of this equation are 2 and -1. As resistance can’t the negative the equivalent resistance between A and B is 2 Ω.

(b)

Let the net current be 2I. This current passes through the 1 Ω resistor. Than splits up equally due to symmetry as there are two 2Ω resistors. Now,  Hence, the current passing through the nearest 2 Ω resistor is 1.5A.

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