AP Physics 1 questions on energy stored in a capacitor

📚 Quick Study Guide

• ⚡ Capacitance (C): The ability of a capacitor to store electric charge. Measured in Farads (F).
• 🔋 Voltage (V): The potential difference across the capacitor plates. Measured in Volts (V).
• ⚛️ Charge (Q): The amount of electric charge stored on the capacitor plates. Measured in Coulombs (C). The relationship between charge, capacitance, and voltage is given by: $Q = CV$.
• 💡 Energy Stored (U): The energy stored in a capacitor is given by the following formulas:
  • $U = \frac{1}{2}CV^2$
  • $U = \frac{1}{2}QV$
  • $U = \frac{Q^2}{2C}$
• 📏 Parallel Plate Capacitor: The capacitance of a parallel plate capacitor is given by: $C = \frac{\epsilon_0 A}{d}$, where $\epsilon_0$ is the permittivity of free space ($8.854 \times 10^{-12} F/m$), $A$ is the area of the plates, and $d$ is the distance between the plates.

🧪 Practice Quiz

1. What is the energy stored in a 20 μF capacitor with a potential difference of 10 V across it?
   1. 0.001 J
   2. 0.01 J
   3. 0.1 J
   4. 1 J
2. A 5 μF capacitor stores 25 μC of charge. What is the voltage across it?
   1. 2 V
   2. 5 V
   3. 10 V
   4. 25 V
3. If the distance between the plates of a parallel plate capacitor is doubled, what happens to its capacitance?
   1. It doubles.
   2. It halves.
   3. It quadruples.
   4. It remains the same.
4. A capacitor is charged to 100 V and stores 0.01 C of charge. What is its capacitance?
   1. 0.0001 F
   2. 0.001 F
   3. 0.01 F
   4. 0.1 F
5. What happens to the energy stored in a capacitor if both the voltage and capacitance are doubled?
   1. It doubles.
   2. It quadruples.
   3. It increases by a factor of eight.
   4. It remains the same.
6. A 10 μF capacitor is connected in parallel with a 5 μF capacitor. What is the equivalent capacitance?
   1. 3.33 μF
   2. 5 μF
   3. 15 μF
   4. 50 μF
7. A parallel-plate capacitor has a capacitance of C. If the area of the plates is doubled and the distance between the plates is halved, what is the new capacitance?
   1. C/4
   2. C/2
   3. 2C
   4. 4C