AP Physics C Electricity and Magnetism: Impedance Multiple Choice Questions

📚 Quick Study Guide

• ⚡️ Impedance (Z) is the total opposition a circuit presents to alternating current. It includes resistance (R) and reactance (X).
• 📐 For a series RLC circuit, impedance is given by: $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $X_L$ is inductive reactance and $X_C$ is capacitive reactance.
• 🧲 Inductive reactance is calculated as: $X_L = \omega L = 2\pi f L$, where L is inductance and f is frequency.
• 🔋 Capacitive reactance is calculated as: $X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}$, where C is capacitance and f is frequency.
• ✍️ Phase angle ($\phi$) between the voltage and current in an AC circuit is given by: $tan(\phi) = \frac{X_L - X_C}{R}$.
• 💡 Resonance occurs when $X_L = X_C$, resulting in minimum impedance ($Z = R$) and maximum current.
• 📊 Power factor is given by $cos(\phi) = \frac{R}{Z}$, indicating how effectively the AC power is being used.

🧪 Practice Quiz

1. A series RLC circuit has a resistance of 10 $\Omega$, an inductive reactance of 20 $\Omega$, and a capacitive reactance of 10 $\Omega$. What is the impedance of the circuit?
   1. 10 $\Omega$
   2. 14.14 $\Omega$
   3. 22.36 $\Omega$
   4. 30 $\Omega$
2. In an RLC circuit, if the inductive reactance is equal to the capacitive reactance, the circuit is said to be at:
   1. Maximum impedance
   2. Resonance
   3. Maximum voltage
   4. Minimum current
3. What is the phase angle in a series RC circuit with a resistance of 30 $\Omega$ and a capacitive reactance of 40 $\Omega$?
   1. 36.87°
   2. -53.13°
   3. 53.13°
   4. -36.87°
4. An inductor of 20 mH is connected to an AC source with a frequency of 50 Hz. What is the inductive reactance?
   1. 3.14 $\Omega$
   2. 6.28 $\Omega$
   3. 9.42 $\Omega$
   4. 12.56 $\Omega$
5. A capacitor of 10 $\mu$F is connected to an AC source with a frequency of 1 kHz. What is the capacitive reactance?
   1. 10 $\Omega$
   2. 15.92 $\Omega$
   3. 20 $\Omega$
   4. 25 $\Omega$
6. In a series RLC circuit, if the resistance is increased, what happens to the power factor?
   1. Increases
   2. Decreases
   3. Remains the same
   4. Becomes zero
7. A series RLC circuit has R = 4 $\Omega$, $X_L$ = 7 $\Omega$, and $X_C$ = 4 $\Omega$. What is the magnitude of the phase angle?
   1. 36.87°
   2. 53.13°
   3. 60°
   4. 45°