question_answer

Nine resistors each of \[1\,k\Omega \] are connected to a battery of 6 V as shown in the circuit given below. What is the total current flowing in the circuit.

A) \[3mA\]            

B) \[\frac{2}{3}mA\]

C) \[\frac{3}{2}mA\]                     

D) \[2\,mA\]

Correct Answer: D

Solution :

The given circuit can be simplified as shown below in circuit \[{{R}_{2}},{{R}_{5}}\] and \[{{R}_{3}},{{R}_{4}}\] are in series and then their resultant is connected parallel. Similarly \[{{R}_{7}},{{R}_{8}}\] and \[{{R}_{6}},{{R}_{9}}\] are in series and their resultant is connected parallel on simplifying this we get their equivalent circuit. Now current in circuit \[I=\frac{V}{R}=\frac{6}{3\times {{10}^{3}}\Omega }\times {{10}^{3}}=2mA\]