Electrical Circuits and Current Concepts

Electrical Circuits

• An electrical circuit is a closed loop path that allows charges to flow.
• Electrical circuits carry energy from one place to another.

Current

• Current is the movement of charge from one region to another.
• Current is measured in amperes (A).
• Current is defined as the amount of charge that passes a given point in a given amount of time.
• The formula for current is I = dQ/dt, where I is current, dQ is the change in charge, and dt is the change in time.
• One ampere is equal to one coulomb per second.
• An electric field in a conductor causes the charges to flow.

Direction of Electrical Current

• Conventionally, electrical current is visualized as positive charges moving in the direction of the electric field. However, it is actually electrons that are moving in the opposite direction.
• A conventional current is treated as a flow of positive charges, regardless of whether the free charges in the conductor are positive, negative, or both.
• In a metallic conductor, the moving charges are electrons, but the current still points in the direction positive charges would flow.

Direction of Current Flow

• The electric field does work on moving charges. The energy is then transferred to the conductor through collisions with the ions in the material, increasing the vibration energy of ions, and the temperature of the conductor.
• The moving charges can be positive or negative in different current-carrying materials.
• Electron flow is the movement of negative charges (electrons) in the opposite direction to the electric field. Conventional current is the flow of positive charges from the positive terminal to the negative terminal. Electron flow is often considered opposite to the conventional current flow.

Current Density

• The current per unit cross-sectional area is called current density (J).
• The formula for current density is J = I / A, where J is current density, I is current, and A is the area.
• The units of current density are amperes per square meter (A/m²).
• Current and current density do not depend on the sign of the charge.

Electrical Current and "Drift" Velocity

• In the absence of an electric field, electrons in a conductor move randomly.
• When an electric field is present (e.g., connecting a battery), electrons are accelerated but collide with atoms in the conductor.
• The combined effect of the electric field and collisions results in a steady-state drift of the electrons—drift velocity—which is much smaller than the speed of the individual electrons.

Resistance and Resistivity

• Resistivity is a measure of how much a material resists the flow of electric current. Materials that resist more than others have a higher resistivity.
• Resistivity is a key factor in determining electrical resistance of a conductor.
• Ohm's Law: When a voltage source is applied across two points in a circuit, electric current will flow between them due to the potential difference. The amount of current is restricted by the resistance present.
• Resistance (R) discourages the flow of charge (the movement of electrons), while voltage encourages it.
• Factors affecting resistance:
  • Material: Different materials have different resistivities (e.g., copper has low resistivity, rubber has high).
  • Length: Longer conductors have higher resistance.
  • Cross-sectional area: Larger cross-sectional area leads to lower resistance.
  • Temperature: Higher temperatures generally lead to higher resistance.

Resistance of a Uniform Cylinder

• For a given shape, the resistance of an object depends on the material from which it is made. Different materials offer different resistances to the flow of charge.
• The resistance R of a uniform cylinder is directly proportional to the resistivity ρ (a material's intrinsic property), its length L, and inversely proportional to its cross-sectional area A. i.e., R = ρL/A
• Several example problems demonstrate how to calculate resistance, current density and drift velocity.

Electrical Conductivity

• Electrical conductivity is the reciprocal of resistivity.
• High resistivity means low conductivity, and vice versa.
• Conductivity is represented by the symbol σ = 1/ρ.

Explore the fundamental concepts of electrical circuits and current in this quiz. Understand how current flows through a closed loop, the measurement of current in amperes, and the direction of electrical current. Test your knowledge on the principles of charge movement and electric fields.