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  • The circuit diagram shown in Fig. consists of a large number of elements (each element has two resistors). The resistance of the resistors in each subsequent element differs by a factor of <im

The circuit diagram shown in Fig. consists of a large number of elements (each element has two resistors). The resistance of the resistors in each subsequent element differs by a factor of \mathrm{K= \frac{1}{2}} from the resistances of the resistors in the previous elements. The equivalent resistance between A and B shown in Fig. is

 

Option: 1

\mathrm{ \frac{R_1-R_2}{2}}


Option: 2

\mathrm{ \frac{\left(R_1-R_2\right)+\sqrt{6 R_1 R_2}}{2}}


Option: 3

\mathrm{\frac{\left(R_1-R_2\right)+\sqrt{R_1^2+R_2^2+6 R_1 R_2}}{2}}


Option: 4

None of these


Answers (1)

best_answer

When each element of the circuit is multiplied by a factor k, then the equivalent resistance also becomes k times. Let the equivalent resistance between A and B be


So the equivalent circuit becomes



\mathrm{X=R_1+\frac{k X R_2}{k X+R_2} }
For \mathrm{ k=\frac{1}{2} \Rightarrow X=\frac{\left(R_1-R_2\right)+\sqrt{R_1^2+R_2^2+6 R_1 R_2}}{2}}

Posted by

Pankaj Sanodiya

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