A) \[4\,A\] or \[6\,A\]
B) \[2\,A\] or \[4\,A\]
C) \[4\,A\]or \[8\,A\]
D) \[2\,A\]or \[6\,A\]
Correct Answer: D
Solution :
[d] Let the unknown resistors are \[{{R}_{2}}\] and \[{{R}_{3}}\]. \[{{i}^{2}}{{R}_{3}}=12;\] \[i{{R}_{2}}=4\] \[{{\left[ \frac{4}{{{R}_{2}}} \right]}^{2}}{{R}_{3}}=12;\] \[\frac{16}{R_{2}^{2}}\times {{R}_{3}}=12;\] \[{{R}_{3}}=\frac{3}{4}R_{2}^{2}\] \[I(I+{{R}_{2}}+{{R}_{3}})=12\] \[\Rightarrow \,\,\,\,\frac{4}{{{R}_{2}}}\left( 1+{{R}_{2}}+\frac{3}{4}R_{2}^{2} \right)=12\] \[\Rightarrow \,\,\,\,3R_{2}^{2}-8{{R}_{2}}+4=0\] \[\Rightarrow \,\,\,\,{{R}_{2}}=2\Omega \] or \[\frac{2}{3}\Omega \] \[I=2A\] or \[6A\]You need to login to perform this action.
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