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(C) Let the equivalent resistance of the infinite network be $R$. Since the network is infinite,adding or removing one repeating unit does not change

Vedclass · Accepted Answer

More than $4\,\Omega $ but less than $12\,\Omega $

Vedclass · Answer

(C) Let the equivalent resistance of the infinite network be $R$. Since the network is infinite,adding or removing one repeating unit does not change the equivalent resistance.The circuit can be viewed as a $2\,\Omega$ resistor in series with the top branch,a $2\,\Omega$ resistor in series with the bottom branch,and the equivalent resistance $R$ in parallel with the vertical $2\,\Omega$ resistor.Thus,the equivalent resistance $R$ is given by:$R = 2 + 2 + \frac{2 	imes R}{2 + R}$$R = 4 + \frac{2R}{2 + R}$Multiplying by $(2 + R)$:$R(2 + R) = 4(2 + R) + 2R$$2R + R^2 = 8 + 4R + 2R$$R^2 - 4R - 8 = 0$Using the quadratic formula $R = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$:$R = \frac{4 \pm \sqrt{(-4)^2 - 4(1)(-8)}}{2(1)}$$R = \frac{4 \pm \sqrt{16 + 32}}{2} = \frac{4 \pm \sqrt{48}}{2} = \frac{4 \pm 4\sqrt{3}}{2} = 2 \pm 2\sqrt{3}$Since resistance cannot be negative,we take the positive root:$R = 2 + 2\sqrt{3} \approx 2 + 2(1.732) = 5.464\,\Omega$.This value is greater than $4\,\Omega$ and less than $12\,\Omega$.

The equivalent resistance of the following infinite network of resistances is

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