For ac circuit shown in figure, R = 100 k and C = 100 pF and the phase difference between and () is 90°. The input signal frequency is rad/sec, where 'x' is ________ . [2025] Figure

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Solution

Q.
For ac circuit shown in figure, R = 100 k $Ω$ and C = 100 pF and the phase difference between $V_{in}$ and ( $V_{B} - V_{A}$ ) is 90°. The input signal frequency is $10^{x}$ rad/sec, where 'x' is ________ . [2025]

Ans.
(5)

Input voltage

$θ + θ = 90 °; θ = 45 °$

$\tan θ = \frac{X_{C}}{R}$

$X_{C} = R \Rightarrow \frac{1}{ω C} = R$

$ω = \frac{1}{R C} = \frac{1}{100 \times 10^{3} \times 100 \times 10^{- 12}} = \frac{10^{12}}{10^{7}} = 10^{5}$

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