Combination of Capacitors?

📌 CONCEPT: When capacitors are connected in parallel, the total capacitance is the sum of individual capacitances, and if a dielectric material is inserted between the plates of one capacitor, its capacitance increases by a factor of the dielectric constant.

📐 RULE / FORMULA: The total capacitance (C_total) of capacitors connected in parallel is given by the formula C_total = C_1 + C_2 +... + C_n, and the capacitance of a capacitor with a dielectric material is given by C = ε_0 * ε_r * C_0, where ε_r is the dielectric constant.

💡 WORKED EXAMPLE: Initially, the total capacitance of the combination is 2 μF + 3 μF + 5 μF = 10 μF. If a dielectric material of dielectric constant 3 is inserted between the plates of the 2 μF capacitor, its new capacitance will be 2 μF * 3 = 6 μF. Now, the total capacitance will be 6 μF + 3 μF + 5 μF = 14 μF.

⚠️ COMMON MISTAKE: Students often forget to consider the effect of inserting a dielectric material on the capacitance of the capacitor it is inserted into, and only calculate the total capacitance without accounting for the increase in capacitance of that particular capacitor.