Alternating Current Circuits — Practice Quiz

A Physics cheat sheet for Alternating Current Circuits — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Capacitive Reactance: Opposition to current flow by a capacitor \(C\) at frequency \(f\).

$$X_C = \frac{1}{2 \pi f C}$$

Inductive Reactance: Opposition to current flow by an inductor \(L\) at frequency \(f\).

$$X_L = 2 \pi f L$$

Impedance (Series RLC): Total opposition to current flow in a series RLC circuit.

$$Z = \sqrt{R^2 + (X_L - X_C)^2}$$

Ohm's Law for AC: Relationship between RMS voltage, RMS current, and impedance.

$$V_{rms} = I_{rms} Z$$

Phase Angle: Angle \(\phi\) by which voltage leads (positive) or lags (negative) current.

$$\tan \phi = \frac{X_L - X_C}{R}$$

Average Power: Power consumed by the circuit. \(\cos \phi\) is the power factor.

$$P = I_{rms} V_{rms} \cos \phi$$

Resonant Frequency: Frequency at which inductive and capacitive reactances are equal ($X_L = X_C$).

$$f_0 = \frac{1}{2 \pi \sqrt{LC}}$$

Practice quiz

  1. A capacitor with capacitance $C = 10 \text{ \mu F}$ is connected to an AC source with frequency $f = 50 \text{ Hz}$. What is its capacitive reactance $X_C$?

    • $31.83 \text{ \Omega}$
    • $3.18 \text{ \Omega}$
    • $318.3 \text{ \Omega}$
    • $0.318 \text{ \Omega}$

    Answer: $31.83 \text{ \Omega}$

  2. An inductor with inductance $L = 200 \text{ mH}$ is connected to an AC source with frequency $f = 60 \text{ Hz}$. What is its inductive reactance $X_L$?

    • $7.54 \text{ \Omega}$
    • $75.40 \text{ \Omega}$
    • $754.0 \text{ \Omega}$
    • $0.754 \text{ \Omega}$

    Answer: $75.40 \text{ \Omega}$

  3. A series RLC circuit has a resistance $R = 30 \text{ \Omega}$, an inductive reactance $X_L = 80 \text{ \Omega}$, and a capacitive reactance $X_C = 40 \text{ \Omega}$. What is the total impedance $Z$ of the circuit?

    • $30 \text{ \Omega}$
    • $40 \text{ \Omega}$
    • $50 \text{ \Omega}$
    • $60 \text{ \Omega}$

    Answer: $50 \text{ \Omega}$

  4. An AC circuit has an impedance $Z = 100 \text{ \Omega}$ and an RMS current $I_{rms} = 1.5 \text{ A}$. What is the RMS voltage $V_{rms}$ across the circuit?

    • $15 \text{ V}$
    • $150 \text{ V}$
    • $1.5 \text{ kV}$
    • $1500 \text{ V}$

    Answer: $150 \text{ V}$

  5. In a series RLC circuit, the resistance is $R = 60 \text{ \Omega}$, inductive reactance $X_L = 120 \text{ \Omega}$, and capacitive reactance $X_C = 40 \text{ \Omega}$. What is the phase angle $\phi$ between the voltage and current?

    • $36.87^\circ$
    • $45^\circ$
    • $53.13^\circ$
    • $60^\circ$

    Answer: $53.13^\circ$

  6. An AC circuit has an RMS voltage $V_{rms} = 240 \text{ V}$, RMS current $I_{rms} = 2 \text{ A}$, and a phase angle $\phi = 60^\circ$. What is the average power $P$ consumed by the circuit?

    • $480 \text{ W}$
    • $240 \text{ W}$
    • $120 \text{ W}$
    • $0 \text{ W}$

    Answer: $240 \text{ W}$

  7. A series LC circuit has an inductor with $L = 100 \text{ mH}$ and a capacitor with $C = 1 \text{ \mu F}$. What is the resonant frequency $f_0$ of the circuit?

    • $159.15 \text{ Hz}$
    • $503.29 \text{ Hz}$
    • $1591.5 \text{ Hz}$
    • $5032.9 \text{ Hz}$

    Answer: $503.29 \text{ Hz}$

  8. At the resonant frequency $f_0$ in a series RLC circuit, which of the following conditions is true?

    • $X_L > X_C$
    • $X_C > X_L$
    • $X_L = X_C$
    • $Z = 0$

    Answer: $X_L = X_C$

  9. A series RLC circuit has $R = 20 \text{ \Omega}$, $L = 50 \text{ mH}$, and $C = 20 \text{ \mu F}$. It is connected to an AC source with $V_{rms} = 120 \text{ V}$ and $f = 100 \text{ Hz}$. What is the RMS current $I_{rms}$ in the circuit?

    • $1.5 \text{ A}$
    • $2.3 \text{ A}$
    • $3.0 \text{ A}$
    • $4.5 \text{ A}$

    Answer: $2.3 \text{ A}$

  10. A series RLC circuit has $R = 40 \text{ \Omega}$, $L = 100 \text{ mH}$, and $C = 50 \text{ \mu F}$. The circuit operates at a frequency $f = 50 \text{ Hz}$. What is the power factor ($\cos \phi$) of the circuit?

    • $0.6$
    • $0.7$
    • $0.78$
    • $0.8$

    Answer: $0.78$

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