AP Physics C: Dielectrics Multiple Choice Questions with Answers

📚 Quick Study Guide

• ⚡ Dielectric Constant ($\kappa$): A dimensionless number indicating how much the electric field is reduced inside the dielectric compared to free space.
• 🔋 Capacitance with Dielectric: The capacitance $C$ of a capacitor increases when a dielectric is inserted: $C = \kappa C_0$, where $C_0$ is the capacitance without the dielectric.
• 💡 Electric Field with Dielectric: The electric field $E$ decreases when a dielectric is inserted: $E = \frac{E_0}{\kappa}$, where $E_0$ is the electric field without the dielectric.
• ⚛️ Potential Difference with Dielectric: The potential difference $V$ decreases when a dielectric is inserted: $V = \frac{V_0}{\kappa}$, where $V_0$ is the potential difference without the dielectric.
• ⚡ Energy Stored: The energy stored in a capacitor changes with a dielectric. Since $U = \frac{1}{2}CV^2$, with the dielectric, $U = \frac{1}{2} \kappa C_0 (\frac{V_0}{\kappa})^2 = \frac{U_0}{\kappa}$ if the charge is kept constant. If the voltage is kept constant, $U = \kappa U_0$.
• 🧪 Dielectric Strength: The maximum electric field a dielectric can withstand before breakdown (insulation failure) occurs.

Practice Quiz

1. A parallel-plate capacitor has a capacitance of $C_0$ in vacuum. When a dielectric material with a dielectric constant of $\kappa = 2$ is inserted between the plates, what is the new capacitance?
   1. $C_0$
   2. $2C_0$
   3. $\frac{C_0}{2}$
   4. $4C_0$
2. A capacitor is charged to a potential difference $V_0$ and then disconnected from the battery. A dielectric is inserted, and the potential difference decreases to $V_0/3$. What is the dielectric constant of the material?
   1. 1
   2. 3
   3. $\frac{1}{3}$
   4. 9
3. A parallel-plate capacitor with a dielectric has a capacitance of 8 $\mu$F. If the dielectric is removed, the capacitance becomes 2 $\mu$F. What is the dielectric constant of the material?
   1. 2
   2. 4
   3. 6
   4. 8
4. A capacitor is connected to a battery, and a dielectric is inserted between the plates. Which of the following quantities remains constant?
   1. Charge
   2. Capacitance
   3. Potential Difference
   4. Energy Stored
5. The electric field between the plates of a capacitor without a dielectric is $E_0$. If a dielectric with a constant $\kappa$ is inserted, what is the new electric field?
   1. $E_0$
   2. $\kappa E_0$
   3. $\frac{E_0}{\kappa}$
   4. $\kappa^2 E_0$
6. A parallel-plate capacitor has an area $A$ and a separation $d$. When a dielectric is inserted, the capacitance increases by a factor of 5. What is the dielectric constant?
   1. 1
   2. 3
   3. 5
   4. 7
7. What happens to the energy stored in a capacitor when a dielectric is inserted while the capacitor is connected to a voltage source?
   1. Increases
   2. Decreases
   3. Stays the same
   4. Becomes zero