Consider the ladder network shown in the figu | vedclass

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(C) Let the effective resistance between $A$ and $B$ be $R_{eq}$.Since the ladder is infinite or has many elements,adding one more section does not ch

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$8$

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(C) Let the effective resistance between $A$ and $B$ be $R_{eq}$.Since the ladder is infinite or has many elements,adding one more section does not change the effective resistance. Thus,the resistance of the entire network to the right of the first section is also $R_{eq}$.The first section consists of two $2 \ \Omega$ resistors in series with the parallel combination of an $8 \ \Omega$ resistor and the rest of the network $(R_{eq})$.So,$R_{eq} = 2 + 2 + \frac{8 	imes R_{eq}}{8 + R_{eq}} = 4 + \frac{8 R_{eq}}{8 + R_{eq}}$.$R_{eq} - 4 = \frac{8 R_{eq}}{8 + R_{eq}}$.$(R_{eq} - 4)(8 + R_{eq}) = 8 R_{eq}$.$8 R_{eq} + R_{eq}^2 - 32 - 4 R_{eq} = 8 R_{eq}$.$R_{eq}^2 - 4 R_{eq} - 32 = 0$.$(R_{eq} - 8)(R_{eq} + 4) = 0$.Since resistance cannot be negative,$R_{eq} = 8 \ \Omega$.For the network to be independent of the number of elements,the terminating resistance $R$ must be equal to the characteristic resistance of the network,which is $R_{eq} = 8 \ \Omega$.

Consider the ladder network shown in the figure. What should be the value of resistance $R$ so that the effective resistance between $A$ and $B$ becomes independent of the number of elements in the combination? ............. $\Omega$

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