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 \[i_{2}^{2}\,t=0.25\,W\] \[\therefore H=12\times 0.25=3W\]You need to login to perform this action.
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