CHAPTER 1. DIRECT CURRENT CIRCUITS8+V(a)I(b)R(c)Figure 1.1: Common circuit elements encountered in DC circuits: a) ideal voltage source,b) ideal current source and c) resistor.1.2.1Electromotive Force (EMF)Charge can ﬂow in a material under the inﬂuence of an external electric ﬁeld. Eventuallythe internal ﬁeld due to the repositioned charge cancels the external electric ﬁeld resultingin zero current ﬂow. To maintain a potential drop (and ﬂow of charge) requires an externalenergy source, ie. EMF (battery, power supply, signal generator, etc.). We will deal withtwo types of EMFs:The ideal voltage source is able to maintain a constant voltage regardless of the currentit must put out (I→∞ is possible).The ideal current source is able to maintain a constant current regardless of the voltageneeded (V→∞ is possible).Because a battery cannot produce an inﬁnite amount of current, a model for the behaviorof a battery is to put an internal resistance in series with an ideal voltage source (zeroresistance). Real-life EMFs can always be approximated with ideal EMFs and appropriatecombinations of other circuit elements.1.2.2GroundA voltage must always be measured relative to some reference point. It is proper to speakof the voltage across an electrical component but we often speak of voltage at a point. It isthen assumed that the reference voltage point is ground.Under strict deﬁnition, ground is the body of the earth. It is an inﬁnite electrical sink.It can accept or supply any reasonable amount of charge without changing its electricalcharacteristics.It is common, but not always necessary, to connect some part of the circuit to earth orground, which is taken, for convenience and by convention, to be at zero volts. Frequently, acommon (or reference) connection of the metal chassis of the instrument suﬃces. Sometimesthere is a common reference voltage that is not at 0 V. Figure 1.2 show some common waysof depicting grounds on a circuit diagram.When neither a ground nor any other voltage reference is shown explicitly on a schematicdiagram, it is useful for purposes of discussion to adopt the convention that the bottom lineon a circuit is at zero potential.