question_answer

Five equal resistances each of value R are connected in a form shown alongside. The equivalent resistance of the network                                                     [Roorkee 1999]

A)         Between the points B and D is R

B)         Between the points B and D is \[\frac{R}{2}\]

C)         Between the points A and C is R                         

D)         Between the points A and C is\[\frac{R}{2}\]

Correct Answer: B , C

Solution :

                                   \[\frac{1}{{{R}_{BD}}}=\frac{1}{2R}+\frac{1}{R}+\frac{1}{2R}\Rightarrow {{R}_{BD}}=\frac{R}{2}\] Between A and C circuit becomes equivalent to balanced Wheatstone bridge so \[{{R}_{AC}}=R\].

Solution :

                               \[\frac{1}{{{R}_{BD}}}=\frac{1}{2R}+\frac{1}{R}+\frac{1}{2R}\Rightarrow {{R}_{BD}}=\frac{R}{2}\] Between A and C circuit becomes equivalent to balanced Wheatstone bridge so \[{{R}_{AC}}=R\].