Impedance Rlc Hard

Hardphysics

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

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$\sqrt (R^{2} + (ω L - 1/ (ω C))^{2})$

R + ωL + 1/(ωC)

$R^{2} + ω L^{2} + 1/ (ω C)^{2}$

R/(ωL - 1/(ωC))

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Subject: physics
Chapter: electromagnetic induction and ac
Topic: impedance rlc hard
Difficulty: Hard
Year: 2025

Solution

Correct Answer:

$\sqrt (R^{2} + (ω L - 1/ (ω C))^{2})$

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 $9 0^{\circ}$ .
$V_{C}$ lags $I$ by $9 0^{\circ}$ . Total reactive component: $X = X_{L} - X_{C} = ω L - \frac{1}{ω C}$ . Combining with resistance $R$ (at $9 0^{\circ}$ to reactance): $Z = R^{2} + X^{2} = R^{2} + (ω L - \frac{1}{ω C})^{2}$ .

This hard difficulty physics question is from the chapter electromagnetic induction and ac, covering the topic of impedance rlc hard. It appeared in the 2025 exam.

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Impedance Rlc Hard

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