Series RLC Circuit Analysis: 30 flashcards
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1. What three components make up a series RLC circuit?
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A resistor (R), an inductor (L), and a capacitor (C), all connected in series.
2. Write the formula for inductive reactance $X_L$.
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$$X_L = \omega L$$ where $\omega$ is angular frequency and $L$ is inductance.
3. Write the formula for capacitive reactance $X_C$.
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$$X_C = \frac{1}{\omega C}$$ where $\omega$ is angular frequency and $C$ is capacitance.
4. What is impedance (Z) in an AC circuit?
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The total effective opposition to current flow, combining resistance and net reactance.
5. State the impedance formula for a series RLC circuit.
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$$Z = \sqrt{R^2 + (X_L - X_C)^2}$$
6. How do you find the current amplitude $I_m$ from voltage amplitude and impedance?
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$$I_m = \frac{V_m}{Z}$$
7. State the phase angle formula for a series RLC circuit.
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$$\phi = \arctan\left(\frac{X_L - X_C}{R}\right)$$
8. What does a negative phase angle $\phi$ tell you about the circuit?
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The current leads the voltage, so the circuit behaves capacitively ($X_C > X_L$).
9. What does a positive phase angle $\phi$ tell you about the circuit?
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The current lags the voltage, so the circuit behaves inductively ($X_L > X_C$).
10. Write the instantaneous current expression for a series RLC circuit.
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$$i(t) = I_m \cos(\omega t + \phi)$$
11. Define power factor in terms of the phase angle.
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$$PF = \cos(\phi)$$ a dimensionless ratio of real power to apparent power.
12. When is the power factor described as leading?
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When the current leads the voltage, which happens when $X_C > X_L$ (capacitive circuit).
13. Which component dissipates average power in a series RLC circuit?
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Only the resistor (R). Inductors and capacitors store and release energy without net dissipation.
14. Give two formulas for average power in a series RLC circuit.
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$$P_{avg} = V_{rms} I_{rms} \cos(\phi) \quad \text{or} \quad P_{avg} = I_{rms}^2 R$$
15. How do you convert peak voltage to RMS voltage?
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$$V_{rms} = \frac{V_m}{\sqrt{2}}$$
16. How do you convert peak current to RMS current?
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$$I_{rms} = \frac{I_m}{\sqrt{2}}$$
17. Why is impedance not simply $R + X_L + X_C$?
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Because $X_L$ and $X_C$ oppose each other and are 90° out of phase with R, so they combine as vectors, not as a plain sum.
18. In the worked example, what were R, $X_L$, and $X_C$?
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$R = 100\,\Omega$, $X_L = 188.5\,\Omega$, and $X_C = 265.25\,\Omega$.
19. In the worked example, what is the impedance Z?
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$Z \approx 126.06\,\Omega$, from $Z = \sqrt{100^2 + (188.5 - 265.25)^2}$.
20. In the worked example, what is the current amplitude $I_m$?
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$I_m = \frac{100}{126.06} \approx 0.7933\,\text{A}$.
21. In the worked example, what is the phase angle $\phi$?
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$\phi = \arctan\left(\frac{-76.75}{100}\right) \approx -37.51^\circ$.
22. In the worked example, what is the power factor?
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$PF = \cos(-37.51^\circ) \approx 0.7933$, and it is a leading power factor.
23. In the worked example, what is the average power dissipated?
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$P_{avg} = I_{rms}^2 R = (0.5609)^2 \times 100 \approx 31.46\,\text{W}$.
24. What is the unit of impedance, reactance, and resistance?
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All three are measured in Ohms ($\Omega$).
25. What is the phase relationship between voltage and current in a purely resistive AC circuit?
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They are in phase, so $\phi = 0$ and $PF = 1$.
26. What happens to $X_L$ and $X_C$ as frequency increases?
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$X_L = \omega L$ increases, while $X_C = \frac{1}{\omega C}$ decreases.
27. Why are RMS values useful in AC power calculations?
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They let AC power be computed with the same formulas as DC, since $P_{avg} = I_{rms}^2 R$ mirrors $P = I^2 R$.
28. What does a power factor close to 1 indicate?
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Efficient power use: most supplied power is converted into useful work rather than circulating reactively.
29. What does a low power factor indicate?
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A large portion of the current is reactive, circulating between source and reactive components instead of doing useful work.
30. Name two practical applications of series RLC circuits.
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Radio tuning circuits and filters (also oscillators and power factor correction).
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