$R_{A}$ and $R_{B}$ are the input resistances of circuits as shown below. The circuits extend infinitely in the direction shown. Which one of the following statements is TRUE?

R_{A} = R_{B}

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R_{A} = R_{B} = 0

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R_{A} < R_{B}

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R_{B} = R_{A} / (1 + R_{A})

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Solution

The correct option is D $R_{B} = R_{A} / (1 + R_{A})$
If the equivalent resistance of first figure is $R_{A}$ then from the second figure, we can see that
$R_{B} = R_{A} | | 1 Ω .$

$R_{B} = \frac{R_{A}}{R_{A} + 1}$

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