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(C) Let the equivalent resistance of the infinite network be $R$. Since the network is infinite,adding one more section of the same resistors will not

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$2$

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(C) Let the equivalent resistance of the infinite network be $R$. Since the network is infinite,adding one more section of the same resistors will not change the equivalent resistance.The circuit can be viewed as $R_1$ in series with the parallel combination of $R_2$ and the equivalent resistance $R$.Therefore,the equivalent resistance $R$ is given by:$R = R_1 + \frac{R \cdot R_2}{R + R_2}$Substituting the given values $R_1 = 1 \, \Omega$ and $R_2 = 2 \, \Omega$:$R = 1 + \frac{2R}{R + 2}$$R = \frac{R + 2 + 2R}{R + 2}$$R(R + 2) = 3R + 2$$R^2 + 2R = 3R + 2$$R^2 - R - 2 = 0$$(R - 2)(R + 1) = 0$Since resistance cannot be negative,we have $R = 2 \, \Omega$.

An infinite ladder network of resistors is shown in the figure. If $R_1 = 1 \, \Omega$ and $R_2 = 2 \, \Omega$,then the equivalent resistance between $A$ and $B$ is ................ $\Omega$.

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