Question 188: AC fundamentals

Question

For ac circuit shown in figure, $\mathrm{R}=100 \mathrm{k} \Omega$ and $\mathrm{C}=100 \mathrm{pF}$ and the phase difference between $\mathrm{V}_{	ext {in }}$ and $\left(\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{A}}ight)$ is $90^{\circ}$. The input signal frequency is $10^x \mathrm{rad} / \mathrm{sec}$, where ' $x$ ' is __________ .

Accepted Answer

Input voltage
$$\begin{aligned}
& 	heta+	heta=90^{\circ} ; 	heta=45^{\circ} \
& 	an 	heta=\frac{\mathrm{X}_{\mathrm{C}}}{\mathrm{R}} \
& \mathrm{X}_{\mathrm{C}}=\mathrm{R} \Rightarrow \frac{1}{\mathrm{~W}_{\mathrm{C}}}=\mathrm{R} \
& \mathrm{~W}=\frac{1}{\mathrm{R}_{\mathrm{C}}}=\frac{1}{100 	imes 10^3 	imes 100 	imes 10^{-12}} \
& =\frac{10^{12}}{10^7}=10^5
\end{aligned}$$

AC fundamentals

Integer / Numeric Answer Type