Question:
In the circuit shown below, the amplitudes of the voltage across the resistor and the capacitor are equal. What is the value of the angular frequency \(\omega_0\) (in rad/s)? (Round off the answer to one decimal place.)
In the circuit shown below, the amplitudes of the voltage across the resistor and the capacitor are equal. What is the value of the angular frequency \(\omega_0\) (in rad/s)? (Round off the answer to one decimal place.)
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In a series \(RC\) circuit, the resistor and capacitor have equal voltage magnitudes when the reactance equals the resistance: \(|X_C|=R\Rightarrow \omega=1/(RC)\).
Updated On: Aug 26, 2025
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Correct Answer: 9.9
Solution and Explanation
Step 1: For a series \(RC\) circuit, the magnitudes of voltages are
\[
|V_R|=I R,\qquad |V_C|=I\left|\frac{1}{j\omega C}\right|=\frac{I}{\omega C}.
\]
Given \(|V_R|=|V_C|\Rightarrow R=\dfrac{1}{\omega_0 C}\), hence
\[
\omega_0=\frac{1}{RC}.
\]
Step 2: Substitute \(R=1\,\text{k}\Omega=1000\,\Omega\) and \(C=100\,\mu\text{F}=1\times10^{-4}\,\text{F}\):
\[
\omega_0=\frac{1}{(1000)(1\times10^{-4})}=\frac{1}{0.1}=10\ \text{rad/s}.
\]
Rounded to one decimal place: \(\boxed{10.0}\).
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