Capacitors in Series

When capacitors are placed in series, the effective plate separation is increased and the total capacitance is less than that of the smallest capacitor. Additionally, the series combination is capable of withstanding a higher total potential difference than any of the individual capacitors. Figure 114 is a simple series circuit. The bottom plate of C1 and the top plate of C2 will be charged by electrostatic induction. The capacitors charge as current is established through the circuit. Since this is a series circuit, the current must be the same at all points. Since the current is the rate of flow of charge, the amount of charge (Q) stored by each capacitor is equal to the total charge.

According to Kirchhoff’s voltage law, the sum of the voltages across the charged capacitors must equal the total voltage, ET. This is expressed as:

Equation E = Q/C can now be substituted into the voltage equation where we now get:

Since the charge on all capacitors is equal, the Q terms can be factored out, leaving us with the equation:

Consider the following example: