CHAPTER 2  >  MATERIALS  >  RELATIONS
Section 2.1
Quantities and Mathematical Operations


Change of charge (∆Q, [Q] = C) of a system.


Determination of transported charge: Integral of charge current from t1 to t2.

Determination of temporal change of charge: Integral of rate of change of charge from t1 to t2.

Definition of spatial difference of electrical potential (delta_phi): Later minus earlier value of potential (taken in a chosen direction).


Definition of voltage (U, [U] = V): negative of potential difference.


Section 2.2

Systems Analysis I: Balance of Charge


Law of balance of electric charge in instantaneous (dynamical) form (for two elements, first one having one flow of charge, second one having three flows).

Junction rule: special case of the law of balance of charge for a junction (node).


Section 2.3

Systems Analysis II: Potentials and Voltages


Loop rule: Sum of all potential differences in a closed electric loop equals zero.


More than one process sharing a potential difference.


Section 2.4

Energy in Electrical Processes and Systems


Determination of electrical power (power of an electric process, rate at which energy is released or used in an electric process).


Determination of a current of energy related to a flow of electric charge.

Section 2.5

Constitutive Laws: Capacitance, Batteries, and Flow


General voltage–charge relation (capacitive relation) of a capacitor. U_C: capacitive potential difference (voltage), alpha_Q: elastance.


General voltage–charge relation (capacitive relation) of a capacitor. U_C: capacitive potential difference (voltage), C_Q: capacitance.


Energy stored in a capacitor (having C = const.).

Characteristic of a battery with internal resistance R_i. U_o: open circuit voltage, U_B: voltage across terminals.


Resistive flow relation for ohmic transport of charge. U_R: resistive potential difference, G: conductance, R: resistance.

Resistance of wire. l: length of wire, r: cross section of wire, rho_el: resistivity of material.


Ohm's law in general form. j_Q: current density, sigma = 1/rho_el: conductivity of material, dphi_el/dx: gradient of electric potential.

Temperature dependence of resistivity (rho_el). alpha: linear temperature coefficient of resistivity, T: temperature.

Equivalent resistance of a number of resistors in series.


Equivalent resistance of a number of resistors in parallel.

Power of an ohmic resistor.


Transport of charge in diodes. U_D: voltage across diode, I_0: saturation current, n: emission coefficient (between 1 and 2). e: elementary charge (1.60·10–19 C), k = 1.38·10–23 J/K is Boltzmann’s constant. T: absolute temperature.


Section 2.6

Dynamical Models and System Behavior


Voltage U_C as a function of time of a capacitor being discharged through a resistor. U_Co: initial capacitive voltage, R: resistance, C: capacitance.


Charging of a capacitor with the help of a battery or other power supply.


Time constant of simple RC system behavior. R: resistance, C: capacitance.