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# In the adjoining infinite circuit, what is the effective resistance as seen by the battery

$\begin {array} {1 1} (A)\;2 \Omega & \quad (B)\;1 \Omega \\ (C)\;1.5 \Omega & \quad (D)\;\large\frac{2}{3} \Omega \end {array}$

Let the resistance of the circuit be R
The adjoining circuit is equivalent to the circuit given in the question
Its equivalent resistance is R
$\Rightarrow \large\frac{2R}{(2+R) }+ 1 = R$
On solving, we get $R = -1\: or\: R = 2$
Since $R>0$ , we get $R = 2\Omega$
Ans : (A)
edited Mar 14, 2014