impedance rlc hard

Question

Magnitude of impedance Z of series RLC at angular frequency ω is:

RankGuru · Accepted Answer

In a series RLC circuit, the total opposition to AC flow is **Impedance** ($Z$). Using the phasor diagram:
- $V_R$ is in phase with $I$.
- $V_L$ leads $I$ by $90^\circ$.
- $V_C$ lags $I$ by $90^\circ$.
Total reactive component: $X = X_L - X_C = \omega L - \frac{1}{\omega C}$.
Combining with resistance $R$ (at $90^\circ$ to reactance):
$Z = \sqrt{R^2 + X^2} = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$.

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impedance rlc hard

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