Solved Examples of Equivalent Capacitance in Series and Parallel Circuits

📚 Quick Study Guide

• ⚡ Capacitance (C): A measure of a capacitor's ability to store electric charge. Measured in Farads (F).
• 🔗 Series Capacitors: Capacitors connected end-to-end. The total equivalent capacitance ($C_{eq}$) is calculated as: $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + ...$
• 🔋 Parallel Capacitors: Capacitors connected side-by-side. The total equivalent capacitance ($C_{eq}$) is calculated as: $C_{eq} = C_1 + C_2 + C_3 + ...$
• 💡 Key Point: In series, the charge (Q) is the same across all capacitors. In parallel, the voltage (V) is the same across all capacitors.
• 📐 Problem Solving Tip: Always draw a circuit diagram to visualize the connections before applying the formulas!

Practice Quiz

1. What is the equivalent capacitance of three capacitors connected in series, with capacitances of 2μF, 4μF, and 8μF respectively?
   1. 1.14 μF
   2. 14 μF
   3. 0.5 μF
   4. 4 μF
2. What is the equivalent capacitance of two capacitors connected in parallel, with capacitances of 3μF and 6μF?
   1. 2 μF
   2. 9 μF
   3. 0.5 μF
   4. 18 μF
3. If two identical capacitors, each with a capacitance of 10μF, are connected in series, what is the equivalent capacitance?
   1. 20 μF
   2. 5 μF
   3. 10 μF
   4. 1 μF
4. If three capacitors, each with a capacitance of 6μF, are connected in parallel, what is the equivalent capacitance?
   1. 2 μF
   2. 18 μF
   3. 6 μF
   4. 36 μF
5. A 4μF capacitor and a 12μF capacitor are connected in series. What is the equivalent capacitance?
   1. 16 μF
   2. 3 μF
   3. 48 μF
   4. 8 μF
6. A 5μF capacitor and a 10μF capacitor are connected in parallel. What is the equivalent capacitance?
   1. 15 μF
   2. 3.33 μF
   3. 50 μF
   4. 2 μF
7. What happens to the equivalent capacitance when more capacitors are added in series?
   1. Increases
   2. Decreases
   3. Remains the same
   4. Becomes infinite