Question

Developing Hypotheses about how Capacitors Combine: In this section of the assignment you'll be using some reasoning based on the relationships shown in Equation 2 to predict how two capacitors ought to combine. Wiring capacitors C_1 and C_2 in parallel: Consider the diagram below. Starting with the idea that the voltage across each of the capacitors is the same, derive an equation for the effective capacitance, What is the effective area. equal to in terms of the areas A, and A2 of the original capacitors? Show your derivation.

Answer 1

Capacitors in parallel combination

   capacitors are used to store some electrical energy, and the capacitance of the capacitors connected in parallel is

we know the relation Q = C*V

   now if two capacitors connected in parallel of capacitance C1,C2

let the total charge is Qt = Q1+Q2

and the voltage across each cpacitor is same so

   Ct.V = C1*V +C2*V

   Ct = C1 + C2

and the capacitance of a capacitor is C = epsilon not *A/d epsilon not is permitivity of free space

               Ct = C1+C2
               Ct = epsilon not/d (A1+A2)

               Ct = epsilon not A_eff/d

so the effective area A is A_eff = A1+A2