Question

Two parallel plate vacuum capacitors have areas A_1 and A_2 and equal plate spacing d. Show that when the capacitors are connected in parallel, the equivalent capacitance is the same as for a single capacitor with plate area A_1+A_2 and spacing d.

Answer 1

Answer

Two parallel plate vacuum capacitors have areas

and

and equal plate spacing

. Show that when the capacitors are connected in parallel, the equivalent capacitance is the same as for a single capacitor with plate area

and spacing

Answer 2

Given:

Area of plate is $(A_1) + (A_2)$

To find : Show that when the capacitors are connected in parallel, the equivalent capacitance is the same as for a single capacitor with plate area $A_1+A_2$  and spacing $d$ .

Solution:

The capacitance of the capacitor $(C_1)$

                       $C_1 = \frac{\epsilon_0 A_1}{d}$

​The capacitance of the capacitor $(C_2)$  

                  $C_2 = \frac{\epsilon_0 A_2}{d}$

When they are in parallel, the equivalent resistance is given by

                     $C = C _1 +C _2$                  

                         =  $\frac{\epsilon_0 A_1}{d} + \frac{\epsilon_0 A_2}{d}$

                        $C= \frac{(A _1 +A _2) \epsilon_0}{d}$

This is the capacitance of plate of area $A _1+A _2$.

Thus, the equivalent capacitance is the same as for a single capacitor with plate area $A 1+A 2$ and spacing $d$.