CHAPTER 1. DIRECT CURRENT CIRCUITS71.1.2Potential DiﬀerenceIt is often more convenient to consider the electrostatic potential V rather than electricﬁeld E as the motivating inﬂuence for the ﬂow of electric charge. The generalized vectorproperties of E are usually unimportant. The change in potential dV across a distance drin an electric ﬁeld isdV =−E · dr.(1.2)A positive charge will move from a higher to a lower potential. The potential is alsoreferred to as the potential diﬀerence or, incorrectly, as just voltage:V = V21 = V2− V1 =V2V1dV.(1.3)Remember that current ﬂowing in a conductor is due to a potential diﬀerence betweenits ends. Electrons move from a point of less positive potential to more positive potentialand the current ﬂows in the opposite direction.The SI unit of potential diﬀerence is the volt (V).1.1.3Resistance and Ohm’s LawFor most materialsV∝ I;V = RI,(1.4)where V = V2−V1 is the voltage across the object, I is the current through the object, andR is a proportionality constant called the resistance of the object. Resistance is a functionof the material and shape of the object, and has SI units of ohms (Ω). It is more commonto ﬁnd units of kΩ and MΩ. The inverse of resistivity is conductivity.Resistor tolerances can be as bad as±20% for general-purpose resistors to±0.1%for ultra-precision resistors.Only wire-wound resistors are capable of ultra-precision applications.The concept of current through and potential across are key to the understanding of andsounding intelligent about electronics.Now comes the most useful visual tool of this course.1.2The Schematic DiagramThe schematic diagram consists of idealized circuit elements each of which represents someproperty of the actual circuit. Figure 1.1 shows some common circuit elements encounteredin DC circuits. A two-terminal network is a circuit that has only two points of interest, sayA and B.