Chapter 14: Analysis of Circuits Containing Batteries and Resistors

Current

Defined as the rate of charge flow per unit time through some surface with units of amps (A \= C/s).

Amps

SI unit of Current

Definition of the magnitude of current

Current density (J)

is a vector field within a wire.

Relationship between current and current density

Relationship between current and current density for the case of a straight wire where the current density is uniform and parallel to the wire

Definition of drift velocity

Charge carrier density (n)

is generally defined as the number of mobile electrons per volume.

Relationship between current density and drift velocity

resistance of the resistor

The potential difference across a resistor is proportional to the current through the resistor, with a ratio defined as the \______.

Ohm’s Law

Ohm’s law

is an experimental observation that V is independent of R and applies to many, but not all, materials.

ohms

SI units for resistance

voltmeter

used to measure a voltage

ammeter

used to measure a current

voltmeter

connected in parallel with circuit elements

ammeter

connected in series

Definition of resistivity

Definition of conductivity

conductivity

is defined as the reciprocal of resistivity

Resistivity

is the property of a certain material

resistance

is the property of a particular object that depends on both the resistivity and the geometry of the object

Resistance of a resistor with length L, cross-sectional area A, and resistivity ρ

Resistors in parallel

Resistor in Series

Node Rule

At any intersection of wires, the total current entering the intersection must equal the total current leaving the intersection.

Loop rule

The sum of the potential differences around any closed loop must be zero.

Node Equation

battery

is a chemical device that boosts the potential energy of electrons flowing through it.

Rate of energy transfer to a resistor

real battery

A \_____ is a series arrangement comprising an ideal resistance-free battery and an internal resistor, even if all its components have resistance.

EMF

voltage of the resistance-free battery to the total electromotive force of the battery.

terminal voltage

refers to the voltage of the terminals of the real battery.

voltage across real batteries is actually a function of the current flowing through them