A) \[{{W}_{1}}>{{W}_{2}}={{W}_{3}}\]
B) \[{{W}_{1}}>{{W}_{2}}>{{W}_{3}}\]
C) \[{{W}_{1}}<{{W}_{2}}={{W}_{3}}\]
D) \[{{W}_{1}}<{{W}_{2}}<{{W}_{3}}\]
Correct Answer: D
Solution :
\[P=\frac{{{V}^{2}}}{R}\] so \[R=\frac{{{V}^{2}}}{P}\] Þ \[{{R}_{1}}=\frac{{{V}^{2}}}{100}\] and \[{{R}_{2}}={{R}_{3}}=\frac{{{V}^{2}}}{60}\] Now \[{{W}_{1}}=\frac{{{(250)}^{2}}}{{{({{R}_{1}}+{{R}_{2}})}^{2}}}.{{R}_{1}}\], \[{{W}_{2}}=\frac{{{(250)}^{2}}}{{{({{R}_{1}}+{{R}_{2}})}^{2}}}.{{R}_{2}}\] and \[{{W}_{3}}=\frac{{{(250)}^{2}}}{{{R}_{3}}}\] \[{{W}_{1}}:{{W}_{2}}:{{W}_{3}}=15:25:64\] or \[{{W}_{1}}<{{W}_{2}}<{{W}_{3}}\]
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