Question

derive the expression for the effective capacity of two capacitors connected in parallel​

Answer 1

capacitors C$\tiny{1}$,C$\tiny{2}$,and CC$\tiny{3}$

are connected in parallel. The same potential is applied across all the three capacitors. Let Q$\tiny{1}$,Q$\tiny{2}$and Q$\tiny{3}$

are charges on the three plates of capacitors such that

Q$\tiny{1}$=C$\tiny{1}$V

Q$\tiny{2}$=C$\tiny{2}$V

Q$\tiny{3}$=C$\tiny{3}$V

The total charge stored is Q=Q$\tiny{1}$+Q$\tiny{2}$+Q$\tiny{3}$

and equivalent capacitance is C$\tiny{eq}$=$\dfrac{Q}{V}$

so,

C$\tiny{eq}$=$\dfrac{Q1+Q2+Q3}{V}$

=$\dfrac{Q1}{V}$+$\dfrac{Q2}{V}$+$\dfrac{Q3}{V}$

C$\tiny{eq}$=C$\tiny{1}$+C$\tiny{2}$+C$\tiny{3}$