### Introduction

Ohm law is a relationship between three physical phenomena: current, voltage, and resistance. Current is defined as the flow of positive charge from a source to a negative charge source. The units for current are C/s for the amount of charge (C) that travels per unit time (s). The ampere (A) is the common unit of current equal to 1 C/s and the symbol for current is I. Current is an intrinsic property, as it depends on other aspects, such as the size of the system. To aptly compare the amount of current for different systems, the current is normalized per area or mass of the system. This is described as the following:

- J = I/A
- J = I/m

Where J is the current density in I/(m·m) or I/g depending on how the systems are compared, I is the current (A), A is the cross-sectional area (m·m), and m is the mass (g). Note that often j is used for current instead of I to prevent confusion with imaginary numbers. Therefore, one should pay attention to the symbols’ definitions, as they can vary case-by-case.

The voltage is another piece of Ohm law that states the amount of work needed to move a charge. The unit for voltage is J/C, which is equal to the ubiquitous unit the Volt (V). The voltage measures the electric potential an object possesses in reference to a charge. By applying a voltage, work is done on the charge which enables the movement of the charge. The amount of charge compared to an individual charge, known as a point charge, can be determined by the following:

- V = kq/(r·r)

Where V is the electric potential (V), k is the constant 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).

The resistance is the opposition to the movement of charge. The resistance is similar to friction effects in flowing water or a sliding object. The units for resistance are Ohms, which is denoted with the capital Greek letter Omega. To calculate the amount of resistance in an object, the following equation can be used:

- R = Rho·l/A

Where R is the resistance (Omega), Rho is the resistivity of the object (Omega·m), l is the length of the object (m), and A is the cross-sectional area of the object (m·m). The resistivity is different for every object and is based on the structure of the material. The calculation for resistivity is outside the scope of this article.

The resistance can also be normalized to provide an apt, case-by-case comparison. The normalized resistance is given by:

- R’ = R·A

Where R is the normalized resistance (Omega·m·m). The resistance, which impedes the flow of charge, is inversely proportional to the current. As the current normalization is per units of area, the resistance normalization is multiplied by units of the cross-sectional area due to the inverse relationship.

The inverse of resistance (1/R) is known as the conductance, which measures the ability of an object to conduct charge given in units of Siemens (S). Further discussion of conductance is outside the scope of this article; however, it is worth noting the inverse relationship conductance has with resistance.

Given the current, voltage, and resistance, Ohm law is defined as:

- V = I·R

Dimensional analysis is needed to ensure consistent units.[1][2][3][4]