question_answer

Three resistors \[1\,\Omega ,\,2\,\Omega \] and \[3\,\Omega \] are connected to form a triangle. Across \[3\,\Omega \] resistor a \[3\,\Omega \] battery is connected. The current through \[3\,\Omega \] resistor is

A)  0.75 A                  

B)  1 A

C)  2 A                                        

D)  1.5 A

Correct Answer: B

Solution :

Required arrangement is shown in figure. The equivalent circuit will look like (since the two resistances of \[1\,\Omega \] and \[2\,\Omega \]. are in series, which form \[3\,\Omega \]  which is in parallel with \[3\,\Omega \]. resistance). Therefore, the effective resistance is                 \[\frac{(1+2)\times 3}{(1+2)+3}=\frac{3}{2}\,\Omega \] \[\therefore \] Current in the circuit,                 \[I=\frac{3}{(3/2)}=2\,A\] \[\therefore \] Current in \[3\,\,\Omega \] resistor \[=\frac{I}{2}=1\,\,A\]