The circuit diagram shown in figure consists of a very large (infinite) number of elements. The resistances of the resistors in each subsequent element differ by a factor of k from the resistances of the resistors in the previous elements. Determine the resistance $${{R}_{AB}}$$ between points A and B if the resistances of the first element are $${{R}_{1}}$$ and$${{R}_{2}}$$. (k=1/2)

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TuteeHUB · Accepted Answer

$$\frac{{{R}_{1}}+{{R}_{2}}+\sqrt{R_{1}^{2}+R_{2}^{2}+6{{R}_{1}}{{R}_{2}}}}{2}$$

TuteeHUB · Answer

$$\frac{{{R}_{1}}-{{R}_{2}}+\sqrt{R_{1}^{2}+R_{2}^{2}+6{{R}_{1}}{{R}_{2}}}}{2}$$

TuteeHUB · Answer

$$\frac{{{R}_{1}}-{{R}_{2}}-\sqrt{R_{1}^{2}+R_{2}^{2}+6{{R}_{1}}{{R}_{2}}}}{2}$$

TuteeHUB · Answer

None of these

1.	The circuit diagram shown in figure consists of a very large (infinite) number of elements. The resistances of the resistors in each subsequent element differ by a factor of k from the resistances of the resistors in the previous elements. Determine the resistance \[{{R}_{AB}}\] between points A and B if the resistances of the first element are \[{{R}_{1}}\] and\[{{R}_{2}}\]. (k=1/2)
A.	\[\frac{{{R}_{1}}-{{R}_{2}}+\sqrt{R_{1}^{2}+R_{2}^{2}+6{{R}_{1}}{{R}_{2}}}}{2}\]
B.	\[\frac{{{R}_{1}}+{{R}_{2}}+\sqrt{R_{1}^{2}+R_{2}^{2}+6{{R}_{1}}{{R}_{2}}}}{2}\]
C.	\[\frac{{{R}_{1}}-{{R}_{2}}-\sqrt{R_{1}^{2}+R_{2}^{2}+6{{R}_{1}}{{R}_{2}}}}{2}\]
D.	None of these
Answer» B. \[\frac{{{R}_{1}}+{{R}_{2}}+\sqrt{R_{1}^{2}+R_{2}^{2}+6{{R}_{1}}{{R}_{2}}}}{2}\]

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