In this article we discuss how capacitors are connected in parallel. We also derive the formula for equivalent capacitance of capacitors connected in parallel.
We can connect capacitors in parallel as shown in the figure below. As indicated in the figure below, three capacitors whose capacitances are C1, C2 and C3 are connected in parallel. A voltage source of V volts is also connected with the parallel combination of capacitors. The voltage across each capacitor is same. This is quite apparent from the figure shown below. Since the capacitance of each capacitor is different, the charge on the plates of each capacitor is different.
Equivalent capacitance of capacitors connected in parallel: “The equivalent capacitance of capacitors connected in parallel is equal to the sum of capacitance of individual capacitors connected in parallel”. This can be proved as follows. Consider the charge stored by each capacitor be represented by Q1, Q2 and Q3 respectively. This charge is related by the capacitance as.
Q1 = C×V1
Q2 = C×V2
Q3 = C×V3
Since the total charge stored by the capacitors is equal to the total charge stored by individual capacitors, total charge can be written as.
Q = Q1 + Q2 + Q3
∴ Q = C1×V + C2×V + C3×V.
∴Q = (C1 + C2 + C3)×V.
∴Q/V = C1 + C2 + C3.
If we denote the equivalent capacitance as C, then C = Q/V. Hence from the above equation we can conclude that the effective capacitance of capacitors connected in parallel is equal to the sum of individual capacitance of each capacitor.
C = C1 + C2 + C3.
We can conclude from the above equation that the equivalent capacitance of capacitors in parallel is always greater than the largest value of capacitance in the connection. The equivalent capacitance is the sum of individual capacitance. Hence whenever you see two or more capacitors in parallel, you can substitute a single capacitor whose value is the sum of individual capacitance. This discussion also holds true in a reverse manner. For example,a single capacitor in a circuit can be substituted by parallel combination of capacitors, as long as their sum add up to the original value.