A) \[{{V}_{1}}=\text{ }{{V}_{2}}=\text{ }{{V}_{3}}\]
B) \[{{V}_{1}}<{{V}_{2}}={{V}_{3}}\]
C) \[{{V}_{1}}>{{V}_{2}}>{{V}_{3}}\]
D) \[{{V}_{1}}>{{V}_{2}}={{V}_{3}}\]
Correct Answer: A
Solution :
Here, \[{{V}_{2}}={{V}_{3}}\] ie, \[{{i}_{2}}\times 1.5R=3R\times {{i}_{3}}\] and \[{{i}_{2}}+{{i}_{3}}=i\] \[\Rightarrow \] \[{{i}_{2}}=\frac{2i}{3}\]and \[{{i}_{3}}=\frac{i}{3}\] Now, \[{{V}_{1}}=IR\] \[{{V}_{2}}=\frac{2i}{3}\times 1.5R=iR\] \[{{V}_{3}}=\frac{i}{3}\times 3R=iR\] ie, \[{{V}_{1}}={{V}_{2}}={{V}_{3}}\]You need to login to perform this action.
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