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The equivalent capacitance of the combination is where C1 and C2 are the capacitance of both capacitors in series.
Let the capacitance of both capacitors be C1 and C2. For a series connected capacitors, same charge flows through the capacitors but different voltage flows through them.
Let Q be the amount of charge in each capacitors,
V be the voltage across each capacitors
C be the capacitance of the capacitor.
Using the formula Q = CV where V = Q/C... (1)
For the large capacitor with capacitance of the capacitor C1,
where is the voltage across
For the small capacitor with capacitance of the capacitor ,
;
where is the voltage across
,
Total voltage V in the circuit will be;
Substituting equation 1, 2 and 3 in equation 4, we have;
Since change Q is the same for both capacitors since they are in series, they will cancel out to finally have;
This gives the equivalent capacitance of the combination.
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