If the input voltage $V_{i}$ to the circuit below is given by $V_{i}(t)=A \cos (2 \pi f t)$, the output voltage is given by $\mathrm{V}_{\mathrm{o}}(\mathrm{t})=\mathrm{B} \cos (2 \pi \mathrm{ft}+\phi)$
Which one of the following four graphs best depict the variation of $\phi$ vs $f$ ?

• A

  
• B

  
• Correct answer
  C

  
• D

  

Solution

Resultant of $V_{C}, V_{R} \& B$ give $V_{i}$ and angle between $V_{i} \& B$ is $\phi .$ When $f$ is very high $X_{C} \rightarrow O$ then $\mathrm{V}_{\mathrm{C}} \rightarrow \mathrm{O} \therefore$ Resultant of $\mathrm{V}_{\mathrm{C}}, \mathrm{V}_{\mathrm{R}} \& \mathrm{~B}$ lie between $\mathrm{B}$ and $\mathrm{V}_{\mathrm{R}}$
B lag behind $\phi$ $\therefore$ At higher frequency $\phi$ become - ve.

Hence, the correct answer is option: 'C'.