Capacitance in Parallel: A Surprising Twist?

📌 CONCEPT: When two capacitors are connected in parallel, their total capacitance is always greater than the individual capacitances due to the principle of superposition in electrostatics.

📐 RULE / FORMULA: The total capacitance (C_total) of two capacitors connected in parallel is given by the formula: 1/C_total = 1/C1 + 1/C2, where C1 and C2 are the individual capacitances.

💡 WORKED EXAMPLE: Consider two capacitors, C1 = 10 μF and C2 = 20 μF. When connected in parallel, the total capacitance is calculated as: 1/C_total = 1/10 μF + 1/20 μF = (2 + 1)/20 μF = 3/20 μF. Therefore, C_total = 20/3 μF ≈ 6.67 μF, which is greater than the individual capacitances.

⚠️ COMMON MISTAKE: Students often incorrectly assume that the total capacitance is simply the sum of the individual capacitances, C_total = C1 + C2, which is not true for capacitors connected in parallel.