question_answer

The equivalent resistance between the points A and B will be (each resistance is 15\[\Omega \])

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, \[{{R}_{1}}=15+10+15=40\Omega \]Between A and B, the resistance of middle part AOB\[{{R}_{2}}=15+15=30\Omega \] Therefore, equivalent resistance between A and B \[\frac{1}{R}=\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{3}}}=\frac{1}{40}+\frac{1}{30}+\frac{1}{15}\] \[=\frac{3+4+8}{120}=\frac{15}{120}\Rightarrow R=\frac{120}{15}=8\Omega \]