Q. 464.7( 6 Votes )
An infinite ladde
Resistors in Series:
Resistors in parallel:
Potential Difference (V) across a resistor of resistance R when current I passes through it is given by Ohm’s law:
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.
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.
Hence, the current passing through the nearest 2 Ω resistor is 1.5A.
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