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  • The effective resistance between points A and C for the network shown in figure is: <img alt="" src="https://cdn.entrance360.com/media/uploads/2023/07/14/physics-53-1.jpg" style="height:1

The effective resistance between points A and C for the network shown in figure is:

Option: 1

\mathrm{\frac{2}{3} R}


Option: 2

\mathrm{\frac{3}{2} R}


Option: 3

2 \mathrm{R}


Option: 4

\frac{1}{2 \mathrm{R}}


Answers (1)

best_answer

As \mathrm{R_{A B}=R_{A O}} and \mathrm{R_{B C}=R_{O C}}, so points O and B will be at same potential and hence, resistance \mathrm{R_{O B}} becomes ineffective. Similarly, \mathrm{R}_{\mathrm{AO}}=\mathrm{R}_{\mathrm{AD}} and \mathrm{R}_{\mathrm{OC}}=\mathrm{R}_{\mathrm{DC}}, resistance \mathrm{R}_{\mathrm{OD}} becomes ineffective. So, excluding \mathrm{R_{B O} \text{ and } R_{O D}}, equivalent resistance \mathrm{R_{e q}} of the given network between points A and C will be given by

\mathrm{\frac{1}{R_{\mathrm{eq}}}=\frac{1}{2 \mathrm{R}}+\frac{1}{2 \mathrm{R}}+\frac{1}{2 \mathrm{R}} \text { i.e., } \mathrm{R}_{\mathrm{eq}}=\frac{2}{3} \mathrm{R}}

Posted by

Devendra Khairwa

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