BodhiAI

Nov. 4, 2019
Grouping of Capacitors

(1) Series grouping

1/C_{eq} = 1/C_{1} + 1/C_{2} + 1/C_{3}

Ceq = (C_{1}^{-1}+ C_{2}^{-1}+ C_{3}^{-1})^{-1}

C_{eq} = C_{1}C_{2}/C_{1}+ C_{2}

V_{1} =( C_{2}/(C_{1}+ C_{2})). V

V_{2} =( C_{1}/(C_{1}+ C_{2})). V

V' =V/n.

(vi) If n identical plates are arranged as shwn below, they constitute (n – 1) capacitors in series. If each capacitor has capacitance ε_{0}Ad then C_{eq} = ε_{0}A/(n-1)a'

(2) Parallel grouping :

Q = Q1 + Q2 + Q3

(ii) C_{eq} = Q1 + Q2 + Q3

Q1 = (C_{1}/(C_{1}+ C_{2})). Q

Q2 = (C_{2}/(C_{1}+ C_{2})). Q

(v) If n identical capacitors are connected in parallel, then Equivalent capacitance C_{eq} = nC and Charge on each capacitor Q’ = Q/n

Capacitance C’ = (n -1)C

C = capacitance of a capacitor = ε_{0}A/d

(vii) If C_{p} is the effective capacity when n identical capacitors are connected in parallel and Cs is their effective capacity when connected in series, then C_{p}/C_{s }= n2 .