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  • Consider an "alternator chain" shown below The equivalent

Consider an "alternator chain" shown below

The equivalent resistance between A and B is

Option: 1

\mathrm{(\sqrt{5}+1) R}


Option: 2

\sqrt{5} \mathrm{R}


Option: 3

\mathrm{(\sqrt{5}-1) R}


Option: 4

\mathrm{(\sqrt{5}+2) R}


Answers (1)

best_answer

The circuit can be redrawn as


when \mathrm{R^{\prime}} is the equivalent resistance between A & B
\mathrm{\therefore \quad R^{\prime}=2 R+\frac{R^{\prime} 2 R}{R^{\prime}+2 R}}

\mathrm{Taking \: \frac{\mathrm{R}^{\prime}}{\mathrm{R}} \equiv \lambda, this \: gives}

\mathrm{\lambda=2+\frac{2 \lambda}{\lambda+2}=\frac{4 \lambda+4}{\lambda+2}}
\mathrm{or, \lambda^{2}+2 \lambda=4 \lambda+4}
\mathrm{or, \lambda^{2}-2 \lambda-4=0}

\mathrm{or, \lambda=(\sqrt{5}+1) R} is the required equivalent resistance.

Posted by

Sayak

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