The circuit diagram shown consists of a large number of element (each element has two resistors R_1 and R

Q: The circuit diagram shown consists of a large number of element (each element has two resistors $R_1$ and $R_2$). The resistance of the resistors in each subsequent element differs by $a$ factor of $K = 1/2$ from the resistance of the resistors in the previous elements. The equivalent reistance between $A$ and $B$ shown in figure is :

c When each element of circuit is multiplied by a factor $k$ then equivalent resistance also become $k$ times. Let the equivalent resistance between $A$ and $B$ be $X$ So, equivalent circuit becomes For $k=\frac{1}{2}$ $\Rightarrow \mathrm{X}=\frac{\left(\mathrm{R}_{1}-\mathrm{R}_{2}\right)+\sqrt{\mathrm{R}_{1}^{2}+\mathrm{R}_{2}^{2}+6 \mathrm{R}_{1} \mathrm{R}_{2}}}{2}$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

The circuit diagram shown consists of a large number of element (each element has two resistors $R_1$ and $R_2$). The resistance of the resistors in each subsequent element differs by $a$ factor of $K = 1/2$ from the resistance of the resistors in the previous elements. The equivalent reistance between $A$ and $B$ shown in figure is :

A$\frac{{{R_1} - {R_2}}}{2}$
B$\frac{{({R_1} - {R_2}) + \sqrt {6\,{R_1}{R_2}} }}{2}$
C$\frac{{({R_1} - {R_2}) + \sqrt {R_1^2\, + R_2^2\, + 6\,{R_1}{R_2}} }}{2}$
D
None of these

Advanced

STD 11 Science
JEE
STD 12 - 3. current electricity
Physics

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