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Capacitance and series equivalent

Short answer

Capacitance is the ratio of charge stored to voltage (C=Q/V), unit farad. For series, charge Q is equal on both capacitors, voltages add: 1/Ceq = 1/C1 + 1/C2, giving Ceq = (C1·C2)/(C1+C2), which is smaller than the smallest individual capacitor.

Define capacitance. Find the equivalent capacitance when two capacitors of capacitance C1 and C2 are connected in series.

Capacitance: the ability of a capacitor to store electric charge. It is the ratio of the charge stored on one plate to the potential difference between the plates: C = Q/V. Unit: farad (F), where 1 F = 1 coulomb per volt.

Series equivalent

 o---| |---| |---o
     C1    C2
  <-V1->  <-V2->
  <------ V ----->

In series, the same charge Q is stored on each capacitor (the charge on the connecting plates is only induced). The total voltage is the sum of the voltages:

V = V1 + V2

V1 = Q/C1, V2 = Q/C2, and for the equivalent capacitor V = Q/Ceq. Substituting:

Q/Ceq = Q/C1 + Q/C2

1/Ceq = 1/C1 + 1/C2

Ceq = (C1 × C2)/(C1 + C2)

The equivalent capacitance is smaller than the smallest individual capacitor. Example: C1 = 6 µF, C2 = 3 µF gives Ceq = 18/9 = 2 µF.

✓ Answer checked by Claude Opus 5.5 (high effort)

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