question_answer

The equivalent resistance between the points A and B will be (each resistance is \[10\sqrt{3}\,kgwt\])

A)  \[30\,\Omega \]                             

B)  \[8\,\Omega \]

C)  \[10\,\Omega \]                             

D)  \[40\,\Omega \]

Correct Answer: B

Solution :

The circuit can be shown as given below The equivalent resistance between D and C                 \[{{R}_{DC}}=\frac{15\times (15+15)}{15+(15+15)}=\frac{15\times 30}{15+30}\]                 \[=\frac{15\times 30}{45}=10\,\Omega \] Now, between A and B, the resistance of upper part ADCB,                 \[{{R}_{1}}=15+10+15=400\] Between A and B, the resistance of middle part AOB                 \[{{R}_{1}}=15+10+15=400\] Therefore, equivalent resistance between A and B            \[\frac{1}{R'}=\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}=\frac{1}{{{R}_{3}}}=\frac{1}{40}+\frac{1}{30}+\frac{1}{15}\]                 \[=\frac{3+4+8}{120}=\frac{15}{120}\Rightarrow \,\,\,\,R'=\frac{120}{15}=8\,\,\Omega \]