# Electric Potential and Capacitance

Article Author:
Kevin Tenny
Article Editor:
Andrew Hanna
Updated:
1/19/2019 8:53:25 PM
PubMed Link:
Electric Potential and Capacitance

## Introduction

Electric potential and capacitance stem from the concept of charge. The charge is the comparison of the number of protons and electrons a material possesses. If there are more protons than electrons, then there is a net positive charge. Conversely, if there are more electrons than protons, there is a net negative charge. An equal number of protons and electrons has a neutral charge. Materials with charge also exhibit electrical forces: opposite charges attract (e.g., positive and negative), and similar charges repel (e.g., positive and positive or negative and negative). The unit of measurement for the charge is a coulomb (C). Protons and electrons individually have a charge of +1.602 E -19 C and -1.602 E -19 C, respectively. The charge values for protons and electrons are considered the elementary charge because the accumulation of microscopic electrons and protons determines the macroscopic charge.

The work done on moving charge is the electric potential. As the name suggests, electric potential measures the change in potential energy of a specific charge. The units for electric potential are joules per coulomb (J/C), which measures the amount of work per charge. The J/C unit is commonly referred to as a volt (V) and is the ubiquitous unit for electric potential. The concept of electric potential is often compared to that of gravitational potential energy. The higher up an object is from the ground, the more gravitational potential energy that object possesses. Similarly, the farther away an object is from a charge, the more electric potential is available. The electric potential from a specific charge is known as a point charge and can be measured explicitly. The equation to determine the electric potential from a specific point charge is:

V = k·q/(r·r)

Where V is the electric potential (V), k is a constant measuring the inverse of the free space permittivity commonly denoted as 8.99 E 9 N (m·m)/(C·C), q is the charge of the point (C), and r is the distance from the point charge (m), which is squared. Dimensional analysis is often needed to ensure all the units are consistent.

The electric potential is inversely related to the square of the distance from the point charge. This suggests that the farther away an object is from the point charge, the electric potential decays quickly. Additionally, if the electric potential is measured at various points around the object, a curve can be generated around the object where each point has the same potential. If two objects containing charges are placed next to each other, then the attractive or repulsive force is present. This is commonly depicted with lines originating from the positively-charged source with an arrow pointing to and terminating at the negatively-charged source. The explanation and applications of electric fields, however, are outside the scope of this article.

While electric potential measures the ability to perform work on a charge, capacitance measures the ability to store charge. The unit of measurement for capacitance is Coulomb per Voltage (C/V), which is the amount of charge present per voltage applied. The Farad (F) is commonly used instead of C/V to measure capacitance. A capacitor is used to hold capacitance and is created when two plates are parallel to each other with each end connected to opposite charge sources. Each charge fills one of the parallel plates generating an electric field between the two. The capacitor can then discharge the charges between the two plates when connected. The equation to determine the capacitance is:

C = e0 · k · A/d

Where C is the capacitance (F), e0 is the permittivity of free space (8.85 E -12 F/m), k is the relative permittivity of the dielectric material between the plates, A is the geometric area of both plates (m·m), and d is the distance between the two plates (m). The capacitance is inversely proportional to the distance, so the greater the separation between the two plates, the smaller the capacitance available. Additionally, the k-value is determined by the material between the parallel plates, and is directly proportional to the capacitance; most capacitors have a solid in between the capacitor to improve capacitance.

## Function

Electric potential and capacitance have a breadth of applications within power generation and energy storage. Every electrical appliance relies on the charge, electric potential, and capacitance to operate. In Roy et al., aspects of electric potential and capacitance are being studied on photogenerated electrical energy to enhance energy storage devices. In this work, Roy et al. study the capacitance of the storage cell because capacitors are temporary batteries that hold a charge. However, the capacitance is just one aspect circuitry needed to create effective electrical devices. Other aspects such as current and resistance are outside the scope of this article.

Properly understanding the electric potential in a system can create materials in novel ways. Aspects of electric potential are used in bone regeneration through polymerization. He et al. used electrical cell culture to create materials used in their study. While this is just one example, the field of electrochemical engineering heavily relies on the accuracy of electric potential in fuel cells and batteries to properly maintain power distribution.

## Issues of Concern

The main issue of concern with electric potential is that it become more rigorous with multiple point charges present. The electric potential can also be a hindrance in many electrochemical-based studies. For example, water electrolysis occurs at 1.23 V, meaning that if more than 1.23 V is applied to a system containing water, the water molecules split into hydrogen and oxygen. Other molecules have voltage thresholds that must be considered when applying a voltage to a system.

Another issue of concern is determining the proper material for a capacitor. If a material produces too much capacitance, then the discharge can destroy the electrical application. If the capacitance is too small, then the application will not work. If the material is not sustainable, then the capacitors will quickly fail and not be economical.

## Clinical Significance

Electric potential is found in nearly every medical device. Each has a specific voltage limit which prevents the device from failing. Electric potential is also found in in the human brain. Human neurons have a voltage of 70 mV on average. Capacitance is also found in nearly every medical device but is the mainstay of defibrillators. Capacitors are temporary batteries that can discharge quicker than regular batteries, which is imperative when a patient undergoes cardiac arrest.

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