Series and Parallel Combination of Capacitors

Why Combinations of Capacitors Needed

The use of combinations of capacitors is similar to the combination of cells (batteries) we use in everyday life. For example, if we need an 8V DC power supply and have four 2V electric cells, we can connect them in series to obtain the desired 8V supply. Capacitors work in a similar way. They allow us to store electrical energy by creating an electric field between two conductors. They are present in almost all electronic devices and are vital for their operation.

Capacitors have fixed capacities, meaning each capacitor has a specific storage capacity. To achieve a desired capacitance for a particular purpose, we can combine capacitors. When we need to increase the overall capacitance in a circuit, we can add a capacitor in parallel to the existing one. On the other hand, if we want to decrease the effective capacitance, we can add a capacitor in series with the existing capacitors. These combinations of capacitors allow us to customize the electrical properties of a circuit to suit our needs.

Series Combination of Capacitors

Let we have C₁ , C₂ and C₃ capacitors connected in Series as shown in figure 1 below. Let V₁ , V₂ and V₃ are the voltages across the capacitors respectively. The “Q” is the charging flowing through the capacitors.

Applying Kirchhoff’s voltage law. \\\;\\V = V_{1}+V_{2}+V_{3}\;\;\;\;\;\;(1)\\\;\\ We know Q = CV\\\;\\\textrm{Thus}\\\;\\V=\frac{Q}{C_{eqv}}\\\;\\\textrm{Similarly}\\\;\\V_{1}=\frac{Q}{C_{1}}\\\;\\V_{2}=\frac{Q}{C_{2}}\\\;\\V_{3}=\frac{Q}{C_{3}}

Putting The Value of V, V₁ , V₂ and V₃ in the equation (1)

\frac{Q}{C_{eqv}}=\frac{Q}{C_1}+\frac{Q}{C_2}+\frac{Q}{C_3}\\\;\\\boxed{\frac{1}{C_{eqv}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}}\\\;\\Above Equation gives equivalent capacitance of series connected capacitors. If “n” capacitors are connected in Series then \\\;\\\boxed{\frac{1}{C_{eqv}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+.......+\frac{1}{C_n}}

Parallel Combination of Capacitors

Let we have C₁ , C₂ and C₃ capacitors connected in parallel and V is voltage across the capacitors. In parallel combination of capacitors voltage across each capacitor is same and charge will be different. Let “Q” is the total charge and Q₁ , Q₂ and Q₃ are the charges across C₁ , C₂ and C₃ capacitors respectively as shown in figure 2 below.

Total Charge , Q = Q₁ + Q₂ + Q₃ \\We know\\ Q = CV \\\;\\ \textrm{Thus} \\\;\\Q = C₁V + C ₂V + C₃V\\\;\\\frac{Q}{V}=C_1+C_2+C_3\\\;\\ C_eqv= C₁ + C ₂ + C₃ \\\;\\\textrm{For "n" capacitors connected in Parallel}\\\;\\\boxed{C_{eqv}=C_1+C_2+C_3.........C_n}

Read Also

1. Resistance in Series and Parallel | Current Divider Rule and Voltage Divider Rule
2. Mutual inductance | Formulae | Coefficient of Coupling | Units
3. Inductor | inductance | Units | Formula