Electric Current, Resistance & Circuits Explained | Chapter 25 of University Physics

Chapter 25 transitions from static charges to moving charges, introducing how electric current flows, how materials resist that flow, and how circuits distribute and use electrical energy. You’ll learn the definitions and units of current and resistance, explore Ohm’s Law, understand how batteries and generators (emf sources) behave in real circuits, and see how microscopic conduction models underpin macroscopic circuit laws.

Watch the full video summary here for detailed walkthroughs of circuit analysis and experimental demonstrations.

Electric Current & Current Density

Electric current (I) is the rate of charge flow:

I = dQ/dt,

with SI unit ampere (A) where 1 A = 1 C/s. Current direction is defined as the flow of positive charge. Current density (J) quantifies how current distributes over a conductor’s cross-sectional area:

J = I/A,

and relates microscopically via carrier density and drift velocity:

J = n q v_d,

where n is charge carrier number density, q their charge, and v_d the drift velocity induced by an electric field.

Resistivity, Conductivity & Ohm’s Law

Resistivity (ρ) measures a material’s opposition to current, defined by:

ρ = E / J,

with unit ohm-meter (Ω·m). Conductivity (σ) is its inverse (σ = 1/ρ). In metals, resistivity typically rises with temperature:

ρ(T) = ρ₀ [1 + α (T – T₀)],

where α is the temperature coefficient of resistivity. Some materials—superconductors—achieve zero resistivity below a critical temperature.

The macroscopic resistance (R) of a uniform conductor of length L and area A is:

R = ρ L / A,

obeying Ohm’s Law for ohmic materials:

V = I R,

where V is potential difference across the resistor.

Electromotive Force & Circuit Basics

Electromotive force (ε) is the energy per unit charge supplied by a source such as a battery or generator. Ideal emf sources maintain constant voltage regardless of load. Real sources include an internal resistance (r), so the terminal voltage under load is:

V_term = ε – I r.

For a complete circuit of external resistance R plus internal r:

I = ε / (R + r).

Energy & Power in Circuits

Electric elements absorb or deliver power (P) given by:

• P = V I
• For a resistor: P = I²R = V² / R

Batteries supplying current I output power P = ε I – I² r. Charging processes reverse sign: work done on the battery is P = ε I + I² r.

Short Circuits & Safety

A short circuit occurs when external resistance is very low, leading to excessive current I ≈ ε / r. This can produce dangerous heating and damage. Circuit protection devices—fuses, circuit breakers—prevent harm by interrupting current under overload.

The Classical Model of Metallic Conduction

In the classical picture, free electrons move randomly and collide with lattice ions. An applied field adds a net drift velocity. The microscopic resistivity formula is:

ρ = m / (n e² τ),

where m and e are the electron mass and charge, n is electron density, and τ the mean time between collisions. Shorter τ means higher resistivity.

Conclusion

Chapter 25 builds the foundation for analyzing DC circuits, linking microscopic conduction to macroscopic laws in complex networks. Master current, resistance, emf, and power relationships to tackle circuits with confidence.

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