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  • A circuit consists of five identical conductors as shown in the figure. The two similar conductors are added as indicated by the dotted lines. The ratio of resistances before and after addition wil

A circuit consists of five identical conductors as shown in the figure. The two similar conductors are added as indicated by the dotted lines. The ratio of resistances before and after addition will be:

Option: 1

\left ( \frac{7}{5} \right )


Option: 2

\left ( \frac{3}{5} \right )


Option: 3

\left ( \frac{5}{3} \right )


Option: 4

\left ( \frac{6}{5} \right )


Answers (1)

best_answer

Before addition,

Total resistance of the circuit is \mathrm{R_1=5\Omega}
After addition the two conductors, the circuit will acquire the form as shown in figure

It is a balanced Wheatstone bridge. Resistance of central conductor is ineffective.
\therefore Total resistance of the circuit is

\mathrm{R}_2=1 \Omega+\frac{(2 \Omega)(2 \Omega)}{(2 \Omega+2 \Omega)}+1 \Omega=1 \Omega+1 \Omega+1 \Omega=3 \Omega

\therefore \quad \frac{\mathrm{R}_1}{\mathrm{R}_2}=\frac{5}{3}

Hence Option 3 is correct.

 

Posted by

shivangi.shekhar

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