To understand how the potential difference between the outer plates of two identical capacitors becomes doubled when they are connected in series after being charged in parallel, let’s break down the process step by step.
Initial Setup of Capacitors
Consider two identical capacitors, each with a capacitance of C. When they are connected in parallel to a battery with a potential difference V, each capacitor charges to the same voltage V. The charge (Q) stored in each capacitor can be calculated using the formula:
Q = C × V
Thus, each capacitor holds a charge of Q = C × V.
Disconnection and Series Connection
After charging, the capacitors are disconnected from the battery. At this point, each capacitor retains the charge Q. Now, when you connect the positive plate of one capacitor to the negative plate of the other, they are effectively in series. The outer plates of the two capacitors are left unconnected.
Understanding Series Connection
In a series connection, the total voltage across the combination is the sum of the voltages across each capacitor. Since both capacitors are identical and each has a voltage of V, the total voltage (V_total) across the series combination is:
V_total = V + V = 2V
Potential Difference Between Outer Plates
Now, let’s focus on the outer plates. The outer plate of the first capacitor (let's call it C1) is at a potential of V, and the outer plate of the second capacitor (C2) is at a potential of -V (since it is connected to the positive plate of C1). The potential difference (V_diff) between these two outer plates is calculated as follows:
V_diff = V (from C1) - (-V) (from C2) = V + V = 2V
Visualizing the Concept
To visualize this, think of the capacitors as two water tanks. When they are filled (charged), each tank has a certain height of water (voltage). When you connect them in series, the heights add up, resulting in a total height (voltage) that is double that of a single tank.
Conclusion
In summary, when the two identical capacitors are charged in parallel and then connected in series, the potential difference between the outer plates becomes double because the voltages across each capacitor add up. This principle is fundamental in understanding how capacitors behave in different configurations and is crucial for applications in circuits.
