A) \[{{v}_{1}}-{{v}_{2}}={{v}_{3}}\]
B) \[{{v}_{1}}={{v}_{2}}-{{v}_{3}}\]
C) \[\frac{1}{{{v}_{1}}}=\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{3}}}\]
D) \[\frac{1}{{{v}_{1}}}=\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{3}}}\]
Correct Answer: A
Solution :
Frequency, \[v=RC\left[ \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right]\] \[{{v}_{1}}=RC\left[ 1-\frac{1}{\infty } \right]=RC\] \[{{v}_{2}}=RC\left[ 1-\frac{1}{4} \right]=\frac{3}{4}RC\] \[{{v}_{3}}=RC\left[ \frac{1}{4}-\frac{1}{\infty } \right]=\frac{RC}{4}\] \[\Rightarrow \] \[{{v}_{1}}-{{v}_{2}}={{v}_{3}}\]
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