AP Physics 2 Questions on Capacitors in Series and Parallel Circuits

📚 Quick Study Guide

• ⚡ Capacitors in Series: When capacitors are connected in series, the total capacitance is less than any of the individual capacitances. The reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances: $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + ...$ The charge on each capacitor is the same.
• 💡 Capacitors in Parallel: When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitances: $C_{eq} = C_1 + C_2 + C_3 + ...$ The voltage across each capacitor is the same.
• 🔋 Charge, Voltage, and Capacitance Relationship: The relationship between charge ($Q$), voltage ($V$), and capacitance ($C$) is given by $Q = CV$.
• 🧮 Energy Stored in a Capacitor: The energy ($U$) stored in a capacitor is given by $U = \frac{1}{2}CV^2 = \frac{1}{2}QV = \frac{1}{2}\frac{Q^2}{C}$.
• 🔍 Dielectrics: Inserting a dielectric material between the plates of a capacitor increases its capacitance. $C' = KC$, where $K$ is the dielectric constant.

🧪 Practice Quiz

1. What is the equivalent capacitance of three capacitors with capacitances of 2 $\mu$F, 4 $\mu$F, and 6 $\mu$F connected in series?
   1. A) 12 $\mu$F
   2. B) 4 $\mu$F
   3. C) 1.09 $\mu$F
   4. D) 0.33 $\mu$F
2. What is the equivalent capacitance of three capacitors with capacitances of 2 $\mu$F, 4 $\mu$F, and 6 $\mu$F connected in parallel?
   1. A) 12 $\mu$F
   2. B) 4 $\mu$F
   3. C) 1.09 $\mu$F
   4. D) 0.33 $\mu$F
3. A 5 $\mu$F capacitor is connected to a 10 V battery. What is the charge stored on the capacitor?
   1. A) 50 $\mu$C
   2. B) 2 $\mu$C
   3. C) 0.5 $\mu$C
   4. D) 500 $\mu$C
4. A 2 $\mu$F capacitor has a charge of 20 $\mu$C. What is the voltage across the capacitor?
   1. A) 10 V
   2. B) 40 V
   3. C) 0.1 V
   4. D) 22 V
5. What is the energy stored in a 4 $\mu$F capacitor with a voltage of 5 V across it?
   1. A) 10 $\mu$J
   2. B) 50 $\mu$J
   3. C) 20 $\mu$J
   4. D) 100 $\mu$J
6. A parallel-plate capacitor has a capacitance of 10 pF. If a dielectric with a dielectric constant of 2 is inserted between the plates, what is the new capacitance?
   1. A) 5 pF
   2. B) 12 pF
   3. C) 20 pF
   4. D) 8 pF
7. Two capacitors, 3 $\mu$F and 6 $\mu$F, are connected in series to a 12 V battery. What is the voltage across the 3 $\mu$F capacitor?
   1. A) 4 V
   2. B) 6 V
   3. C) 8 V
   4. D) 12 V