Combinations of Capacitors C QV Series Capacitors The

Combinations of Capacitors C = Q/V

Series Capacitors • The magnitude of the charge on both capacitors must be the same. • ΔV across both capacitors is equal to the sum of the ΔV across each capacitor. • Vab = Vam + Vmb

Capacitors in Series Capacitors in series all have the same charge; the total potential difference is the sum of the potentials across each capacitor. Vs = V 1 + V 2 + V 3, or Q/Cs = Q/C 1 + Q/C 2 + Q/C 3 Note that this gives the inverse of the capacitance.

Parallel Capacitors • Upper plates of both are at a common potential; lower plates at common potential. • Same potential difference across both capacitors.

Capacitors in Parallel Capacitors in parallel all have the same potential difference; the total charge is the sum of the charge on each. Qp = Q 1 + Q 2 + Q 3 , Cancel V or C p. V = C 1 V + C 2 V + C 3 V

Capacitors in Parallel We can picture capacitors in parallel as forming one capacitor with a larger area:

Equivalent Capacitance Parallel capacitors Series Capacitors • Ceq = C 1 + C 2 + C 3… • Qtotal = Q 1 + Q 2 + Q 3…

Find the equivalent capacitance of the group of capacitors. Circuit reduction method. 1) C 1 and C 2 in parallel: Cp = C 12 = C 1 + C 2 = 0. 10µF + 0. 20µF = 0. 30µF 2) C 12 and C 3 in series: 1/Cs = 1/C 12 + 1/C 3 = 1/0. 30µF + 1/0. 60µF = 2/0. 60µF + 1/0. 60µF = 3/0. 60µF Cs = 0. 20µF Find the voltage across each capacitor. Charge on equivalent capacitance: Q = 0. 20 x 10 -6 F x 12 V = 2. 4 x 10 -6 C That is also the charge on C 3 and C 12 because they are connected in series. V 3 = Q/C 3 = (2. 4 x 10 -6 C)/(6 x 10 -7 F) = 4 V V 12 = V-V 3 = 12 V – 4 V = 8 V