Current Electricity - Study Notes

Chapter Summary

This chapter moves from stationary charges to the behavior of charges in motion. It explores how an electric field within a conductor drives free electrons to create a steady flow known as electric current. The study covers fundamental laws like Ohm's Law and Kirchhoff's Rules, which govern circuit behavior, and examines the practical effects of current, such as heating and thermoelectric phenomena.

Learning Objectives

• Understand the mechanism of charge flow in metallic conductors and define drift velocity.
• Apply Ohm's law and explore the relationship between resistance, resistivity, and temperature.
• Calculate equivalent resistance for series and parallel combinations.
• Master Kirchhoff’s rules to solve complex circuit networks.
• Analyze electrical power, energy, and the heating effects of current.
• Describe thermoelectric effects including the Seebeck, Peltier, and Thomson effects.

Key Concepts and Definitions

Electric Current (I): The rate at which net charge flows through a given cross-sectional area, measured in Amperes (A). I = dQ/dt.

Drift Velocity (v_d): The slow average velocity acquired by free electrons inside a conductor when subjected to an external electric field.

Current Density (J): A vector quantity representing the amount of current flowing per unit area of cross-section perpendicular to the flow direction.

Electrical Resistivity (ρ): A property of a material that quantifies how strongly it resists electric current. For a conductor of unit length and unit area, the resistance equals the resistivity.

Kirchhoff's Current Rule: Based on the law of conservation of charge, it states that the algebraic sum of currents meeting at any junction in a circuit is zero.

Kirchhoff's Voltage Rule: Based on the law of conservation of energy, it states that the algebraic sum of the products of current and resistance in each part of a closed loop is equal to the total emf in that loop.

Worked Methods

Calculating Resistance from Physical Dimensions: Use the formula R = ρ(l/A). Remember that if a wire is stretched, its length increases while its area decreases, keeping volume constant. This significantly changes the resistance.

Solving Complex Networks: Identify junctions and loops. Apply the Current Rule at junctions to reduce variables, then apply the Voltage Rule to closed loops to create independent linear equations.

Determining Internal Resistance: Connect a high-resistance voltmeter across a cell to measure its emf (ε). Then connect a known external resistance (R) and measure the terminal voltage (V). The internal resistance (r) can be found using the drop in potential: r = R((ε/V) - 1).

Common Exam Traps

• Electron Source: Batteries are not sources of electrons; they are sources of electrical energy that provide the potential difference needed to move existing electrons in the circuit.
• Scalar vs. Vector: Electric current is a scalar because it does not follow vector addition, even though it has direction. However, current density is a vector.
• Terminal Voltage vs. EMF: The voltage across a battery is only equal to its emf when no current is flowing. Once a circuit is closed, internal resistance causes the terminal voltage to drop.

Exam Tips

• Always convert time to seconds when calculating charge or energy (e.g., minutes to seconds).
• In power problems, use P = V²/R for parallel circuits where voltage is constant, and P = I²R for series circuits where current is constant.
• When applying Kirchhoff's rules, be consistent with sign conventions for current direction and emf polarities.
• Note that resistivity decreases with temperature for semiconductors, which is opposite to the behavior of metallic conductors.