Combining capacitors
Section: Capacitance | Syllabus: Cambridge AS Level Physics 9702
Capacitors in Parallel When capacitors are connected in parallel , they all have the same potential difference V across their plates. The total charge stored is the sum of the individual charges. Figure 19.15: Capacitors in Parallel Three capacitors connected in parallel across a common potential difference V.
Each capacitor has the same P.D. but stores different charges. 1. Q = Q_1 + Q_2 + Q_3 2. Since Q = CV: CV = C_1V + C_2V + C_3V 3. Dividing by V gives the combined capacitance: C = C_1 + C_2 + C_3 + Connecting capacitors in parallel effectively increases the plate area, thus increasing the capacitance.
Capacitors in Series When capacitors are connected in series , the charge Q on each capacitor is the same. This is because charge is induced from one plate to the next. The total P.D. V is the sum of the individual P.D.s.
Figure 19.16: Capacitors in Series Three capacitors connected in series. Each capacitor stores the same charge Q but has different potential differences across it. 1. V = V_1 + V_2 + V_3 2. Since V = Q/C: Q/C = Q/C_1 + Q/C_2 + Q/C_3 3.
Dividing by Q gives the reciprocal relationship: 1/C = 1/C_1 + 1/C_2 + 1/C_3 + Worked Examples Worked Example: Mixed Capacitance Calculation Question: Determine the total capacitance between terminals X and Y for a 2 pF and 6 pF capacitor in series, connected in parallel with a 3 pF capacitor.
Solution Series branch: 1/C_s = 1/2 + 1/6 = 4/6 C_s = 1.5 pF. Parallel combination: C_total = C_s + 3 = 1.5 + 3 = 4.5 pF. Maximum Safe Potential Difference Capacitors are rated for a maximum safe voltage.
When combined in series, the total safe P.D. is the sum of the allowed p.d.s across each capacitor (provided the charge is shared appropriately).
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