Solved Examples: Energy Stored in Series and Parallel Capacitors

📚 Quick Study Guide

🔍 Capacitance: The ability of a capacitor to store electrical energy. Measured in Farads (F). Symbol: C. 💡 Energy Stored in a Capacitor: $U = \frac{1}{2}CV^2$, where U is the energy in Joules, C is the capacitance in Farads, and V is the voltage in Volts. ⚡️ Series Capacitors: The reciprocal of the equivalent capacitance is the sum of the reciprocals of individual capacitances: $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + ...$. Charge is the same across all capacitors in series. 🔋 Parallel Capacitors: The equivalent capacitance is the sum of the individual capacitances: $C_{eq} = C_1 + C_2 + C_3 + ...$. Voltage is the same across all capacitors in parallel. 📈 Total Energy in Series: $U_{total} = U_1 + U_2 + U_3 + ...$. Since charge is constant, energy is inversely proportional to capacitance ($U = \frac{Q^2}{2C}$). 📉 Total Energy in Parallel: $U_{total} = U_1 + U_2 + U_3 + ...$. Since voltage is constant, energy is directly proportional to capacitance.

🧪 Practice Quiz

1. Question 1: Three capacitors with capacitances of 2 μF, 4 μF, and 6 μF are connected in series. What is the equivalent capacitance of the combination?
   1. 12 μF
   2. 4 μF
   3. $\frac{12}{11}$ μF
   4. $\frac{11}{12}$ μF
2. Question 2: The series combination of the three capacitors in Question 1 is connected to a 12V battery. What is the total energy stored in the circuit?
   1. 864 μJ
   2. 66 μJ
   3. 6 μJ
   4. 86 μJ
3. Question 3: Three capacitors with capacitances of 2 μF, 4 μF, and 6 μF are connected in parallel. What is the equivalent capacitance of the combination?
   1. 12 μF
   2. 4 μF
   3. $\frac{12}{11}$ μF
   4. $\frac{11}{12}$ μF
4. Question 4: The parallel combination of the three capacitors in Question 3 is connected to a 12V battery. What is the total energy stored in the circuit?
   1. 864 μJ
   2. 66 μJ
   3. 86 μJ
   4. 6 μJ
5. Question 5: Two capacitors, C1 = 3 μF and C2 = 6 μF, are connected in series to a 10V battery. What is the charge on C1?
   1. 20 μC
   2. 30 μC
   3. 60 μC
   4. 90 μC
6. Question 6: Two capacitors, C1 = 3 μF and C2 = 6 μF, are connected in parallel to a 10V battery. What is the energy stored in C2?
   1. 300 μJ
   2. 600 μJ
   3. 900 μJ
   4. 150 μJ
7. Question 7: If two identical capacitors are first connected in series and then in parallel across the same voltage source, what is the ratio of the energy stored in the parallel configuration to the energy stored in the series configuration?
   1. 1:4
   2. 1:2
   3. 2:1
   4. 4:1