question_answer

Three resistors 1\[\Omega \], 2\[\Omega \] and 3\[\Omega \] are connected to form a triangle. Across 3\[\Omega \] resistor a 3 V 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,                 \[I=\frac{3}{(3/2)}=2A\]                \[\therefore \]Current in\[3\Omega \]resistor\[=\frac{I}{2}=1A\]