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`.

Explanation

To solve the problem, we need to derive the equivalent capacitance of two parallel plate capacitors with areas \( A_1 \) and \( A_2 \) and equal plate spacing \( d \) when they are connected in parallel.

### Step-by-Step Solution:

1. **Understand the Capacitance Formula**:
The capacitance \( C \) of a parallel plate capacitor in a vacuum is given by the formula:
\[
C = \frac{\epsilon_0 A}{d}
...