A) 169 : 16 : 256
B) 256 : 16 : 169
C) 256 : 16 : 196
D) 256 : 196 : 16
Correct Answer: B
Solution :
\[{{I}_{A}}=R_{1}^{2}\] \[{{I}_{B}}={{({{R}_{1}}-{{R}_{2}})}^{2}}=R_{1}^{2}{{\left( 1-\frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{2}}=R_{1}^{2}{{\left( 1-\frac{3}{4} \right)}^{2}}=\frac{R_{1}^{2}}{16}\] \[{{I}_{C}}={{({{R}_{1}}-{{R}_{2}}+{{R}_{3}})}^{2}}\]\[=R_{1}^{2}{{\left( 1-\frac{{{R}_{2}}}{{{R}_{1}}}+\frac{{{R}_{3}}}{{{R}_{1}}} \right)}^{2}}\] \[=R_{1}^{2}{{\left( 1-\frac{{{R}_{2}}}{{{R}_{1}}}+\frac{{{R}_{3}}}{{{R}_{2}}}\times \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{2}}\] \[=R_{1}^{2}{{\left( 1-\frac{3}{4}+\frac{3}{4}\times \frac{3}{4} \right)}^{2}}\]\[={{\left( \frac{13}{16} \right)}^{2}}R_{1}^{2}=\frac{169}{256}R_{1}^{2}\] \[\therefore \,\,\,{{I}_{A}}:{{I}_{B}}:{{I}_{C}}=R_{1}^{2}:\frac{R_{1}^{2}}{16}:\frac{169}{256}R_{1}^{2}=256:16:169\]You need to login to perform this action.
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