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Physics-

General

Easy

Question

An infinite ladder network is arranged with resistances R and 2 R as shown. The effective resistance between terminals A and B is

$\infty$
R
2 R
3 R

The correct answer is: 2 R

Let equivalent resistance between A and B is R', so given circuit can be reduced as follows

$R ´ equals R plus fraction numerator 2 R cross times R to the power of ´ end exponent over denominator left parenthesis 2 R plus R to the power of ´ end exponent right parenthesis end fraction rightwards double arrow R to the power of ´ 2 end exponent minus R R to the power of ´ end exponent minus 2 R to the power of 2 end exponent equals 0$
On solving the equation we get $R ´ equals 2 R$ .

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