question_answer

                Power dissipated across the \[8\,\,\Omega \] resistor in the circuit shown here is 2 W. The power dissipated in watt units across the \[3\,\,\Omega \] resistor is:                                                                                                                        

A)                  2.0        

B)                  1.0        

C)                  0.5      

D)                  3.0

Correct Answer: D

Solution :

                Resistance \[1\Omega \] and \[3\,\,\Omega \] are connected in series, so effective resistance                 \[R'=1+3=4\Omega \]                 Now, R? and \[8\,\,\Omega \] are in parallel. We know that potential difference across resistances in parallel order is same                                 Hence,  \[R'\times {{i}_{1}}=8{{i}_{2}}\] \[or4\times {{i}_{1}}=8{{i}_{2}}\] \[or{{i}_{1}}=\frac{8}{4}{{i}_{2}}=2{{i}_{2}}\] \[or{{i}_{1}}=2{{i}_{2}}....(i)\]                 Power dissipated across \[8\,\,\Omega \] resistance is                 \[i_{2}^{2}(8)\,t=2W\]                 \[ori_{2}^{2}\,t=\frac{2}{8}\,=0.25\,W....(ii)\]                 Power dissipated across \[3\,\,\Omega \] resistance is                 \[H=i_{1}^{2}\,(3)\,t\]                 \[={{(2{{i}_{2}})}^{2}}\,(3)t\]                 \[=12\,i_{2}^{2}\,t\]                 but         \[i_{2}^{2}\,t=0.25\,W\]                 \[\therefore H=12\times 0.25=3W\]