Electric Current and DC Circuit Analysis

Electric Current and DC Circuit Analysis

Learning Outcomes

• Explain electric current at macroscopic and microscopic levels

• Apply Ohm's Law correctly

• Distinguish resistance and resistivity

• Analyse DC circuits using Kirchhoff's laws

Electric Current

Definition and Properties

Electric current is a fundamental concept in physics, describing the flow of electric charge through a conductor. It is essential for understanding how electrical circuits operate.

• Electric current is defined as the rate of flow of electric charge.

• The mathematical expression for current is: $I = \frac{dQ}{dt}$

• The SI unit of electric current is the Ampere (A).

• Conventional current is considered to flow from the positive terminal to the negative terminal of a power source.

Example: If 2 Coulombs of charge pass through a wire in 4 seconds, the current is $I = \frac{2}{4} = 0.5$ A.

Microscopic View: Drift Velocity

Electron Motion in Conductors

At the microscopic level, electric current arises from the movement of electrons in a conductor. The concept of drift velocity helps explain how these electrons contribute to current.

• Electrons move randomly due to thermal energy, but an applied electric field causes a net movement called drift velocity.

• The relationship between current and drift velocity is: $I = nqA v_d$ where:

  • $n$ = number of charge carriers per unit volume

  • $q$ = charge of each carrier

  • $A$ = cross-sectional area of the conductor

  • $v_d$ = drift velocity

• Drift speed is typically very slow, but the electric signal propagates rapidly through the conductor.

Example: In a copper wire, even though electrons drift slowly, a light bulb turns on almost instantly when the switch is closed due to the rapid propagation of the electric field.

Conductors, Insulators, and Semiconductors

Classification of Materials

Materials are classified based on their ability to conduct electric current:

• Conductors: Contain many free electrons that can move easily (e.g., copper (Cu), aluminum (Al)).

• Insulators: Have no free charge carriers, so they do not conduct electricity (e.g., rubber, glass).

• Semiconductors: Have conductivity between conductors and insulators, and their conductivity can be controlled (e.g., silicon (Si), germanium (Ge)).

Example: Silicon is widely used in electronic devices because its conductivity can be precisely controlled by doping.

Ohm's Law

Relationship Between Voltage, Current, and Resistance

Ohm's Law is a fundamental principle that relates the voltage across a conductor to the current flowing through it and its resistance.

• At constant temperature, the voltage across a conductor is proportional to the current:

$V \propto I$

• The mathematical form of Ohm's Law is: $V = IR$ where $V$ is voltage, $I$ is current, and $R$ is resistance.

• Ohm's Law applies to ohmic materials (materials with a constant resistance).

• Non-ohmic devices (e.g., diodes, filament bulbs) show non-linear current-voltage behavior.

Example: If a resistor has $R = 10\ \Omega$ and the current is $2$A, then$V = 2 \times 10 = 20$ V.

Resistance and Resistivity

Dependence on Material and Geometry

Resistance is a measure of how much a material opposes the flow of electric current. It depends on both the material and the physical dimensions of the conductor.

• The resistance $R$ of a uniform conductor is given by: $R = \rho \frac{L}{A}$ where:

  • $\rho$ = resistivity of the material (a property of the material)

  • $L$ = length of the conductor

  • $A$ = cross-sectional area

• Resistivity $\rho$ is a material property, measured in $\Omega \cdot \text{m}$.

• Resistance is measured in Ohms ($\Omega$).

Example: A copper wire of length 2 m and cross-sectional area $1 \times 10^{-6}$ m$^2$ with $\rho = 1.7 \times 10^{-8}\ \Omega \cdot \text{m}$ has $R = 1.7 \times 10^{-8} \times \frac{2}{1 \times 10^{-6}} = 0.034\ \Omega$.

Additional info: Kirchhoff's laws, mentioned in the learning outcomes, are essential for analyzing complex DC circuits but are not detailed in these slides. They include Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL).