Question

You have two capacitors and want to connect them Across a voltage source (battery) to store the maximum amount of Energy. Should they be connected in series or in parallel?

Short answer

The two capacitors should to connect in parallel because the potential energy in the given parallel connection is 4 times the potential energy in the series connection

Step-by-step solution

About Voltage source battery

A voltage source is a two-terminal device which can maintain a fixed voltage. An ideal voltage source can maintain the fixed voltage independent of the load resistance or the output current.

:Determine how to connect the capacitor for maximum store of energy

Concept:

As equation 24.9 mention, the potential energy stored in a capacitor is given by

Where Q is the magnitude of the charge on each plate, C is the capacitance and V is the potential difference between plates.

As equation 24.2 mention, the capacitance of a parallel plate capacitor in a vacuum is given by

Where A is the area of each plate and d is the distance between the two plates Substituting from the previous calculation then we get

:Determine the potential energy in the parrel connection

Solution:

The two capacitors should connect in parallel. As equation 24.7 mention, the equivalent capacitance of the two capacitors connected in parallel is given by

As we mentioned before in the concept session , the potential energy stored is given by

Determine the Potential energy in parallel connection

Solution:

As equation 24.5 mention, the equivalent capacitance of the two capacitors connected in series is given by

As we mentioned before in the concept session, the potential energy stored is given by

So, the potential energy in the parallel connection is 4 times the potential energy in the series connection.

.Therefore ,The two capacitors should to connect in parallel because the potential energy in the given parallel connection is 4 times the potential energy in the series connection