Q21CQ - College Physics (Urone)

Question

If you wish to store a large amount of energy in a capacitor bank, would you connect capacitors in series or parallel? Explain

Step-by-Step Solution

Answer

The capacitors should be connected in parallel. 

Step 1 Definition of capacitor

A capacitor is a device that has the ability to store energy, in the form of an electric field, inside. Capacitance is used to describe this ability of a capacitor.

Step 2: Basic concept and principles of the capacitor

When a capacitor with capacitance C is charged to a potential difference $∆\mathrm{V}$, the electric potential energy E stored in the capacitor is:

$\mathbf{E}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{C}\mathbf{(}\mathbf{\Delta V}{\mathbf{)}}^{\mathbf{2}}$……. (1)

Capacitors in Parallel: 

When capacitors with capacitances C₁, C₂ …are connected in parallel, the equivalent capacitance C_eq equals the sum of the individual capacitances:

${\mathbf{\text{C}}}_{\mathbf{eq}}\mathbf{=}{\mathbf{C}}_{\mathbf{1}}\mathbf{+}{\mathbf{C}}_{\mathbf{2}}\mathbf{+}\mathbf{\dots }\mathbf{\dots }$

Step 3: Determining how to connect the capacitors to store a large amount of energy

If we want to store a significant amount of energy in a capacitor bank, we must figure out how to connect capacitors. The voltage \(\Delta V\) across the capacitor must be constant since the capacitors are connected to a battery. As a result, the energy stored in the circuit is directly proportional to the equivalent capacitance of the circuit, according to Equation (1).

The equivalent capacitance of the circuit grows as the number of capacitors in parallel increases, and thus the energy stored in the circuit increases.

Therefore, the capacitors should be connected in parallel.