Electric current Knowledge-Based Study

Study notes

1. What is Electric Current?

   Electric current is the net rate of flow of electric charge through a given cross-sectional area of a conductor over time. If a net charge $\Delta Q$ passes through a cross section in a time interval $\Delta t$, the average electric current $I$ is defined as:

   $$I = \frac{\Delta Q}{\Delta t}$$

   Units of Current

   In the International System of Units (SI):

   • Charge ($\Delta Q$) is measured in coulombs ($\text{C}$).
   • Time ($\Delta t$) is measured in seconds ($\text{s}$).
   • Current ($I$) is measured in amperes ($\text{A}$), where $1\text{ A} = 1\text{ C/s}$.

   Charge Carriers in Different Media

   The particles that move and transport electric charge are called charge carriers:

   • Solid conductors (metals): Free conduction electrons carry negative charge while positive atomic nuclei remain fixed in the crystal lattice.
   • Electrolytes: Both positive ions (cations) and negative ions (anions) move in opposite directions to establish current.
   • Gases / Plasmas: Positive ions, negative ions, and free electrons can all act as charge carriers under high electric fields.

   Conventional Current vs. Electron Flow

   When studying electric circuits, it is essential to distinguish between the physical motion of charge carriers and the standard definition of current direction.

   Conventional Current

   Historically, electric current was defined before the discovery of the electron. By international convention:

   • Conventional current is defined as the direction in which positive charges would move under the influence of an electric field.
   • In an external circuit connected to a direct-current (DC) power source, conventional current leaves the positive terminal (higher potential) and enters the negative terminal (lower potential).

   Actual Electron Flow in Metallic Conductors

   In metallic wires, the actual mobile carriers are negatively charged electrons:

   • Because electrons have a negative charge, the electrostatic force on them is opposite to the direction of the electric field.
   • Therefore, electrons drift from the negative terminal (lower potential) toward the positive terminal (higher potential).
   • Despite electron flow moving opposite to conventional current, all standard circuit analysis laws and formulas (such as Ohm's law and Kirchhoff's rules) are formulated using conventional current.

   Quantization of Charge in Electric Current

   Electric charge is quantized, meaning any net observable charge is an integer multiple of the elementary charge $e$:

   $$\Delta Q = n \cdot e$$

   where $n$ is the number of charge carriers and $e \approx 1.6 \times 10^{-19}\text{ C}$.

   Expressing Current in Terms of Carrier Count

   Substituting the quantized charge into the current equation gives:

   $$I = \frac{n \cdot e}{\Delta t}$$

   This relationship allows us to determine the microscopic quantity of moving particles from a macroscopic measurement of current.

   Electrolyte Solutions: Total Charge Transfer

   In an electrolytic cell where both positive and negative ions move, both carrier types contribute to the total current. If $n_1$ positive ions of charge $q_1$ pass a cross section in one direction and $n_2$ negative ions of charge $q_2$ pass in the opposite direction during time $\Delta t$, the net charge transferred across the cross section is the sum of their magnitudes:

   $$\Delta Q_{\text{total}} = |q_1| + |q_2|$$

   Because opposite charges moving in opposite directions produce electric currents that add constructively, the resulting total current is:

   $$I = \frac{|q_1| + |q_2|}{\Delta t}$$