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\[=\frac{I}{2}=1A\]