2 Alternating Current Circuits

Chapter 2 Alternating Current Circuits

Physics Lecture Notes – Phys 395 Electronics Book
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Physics Lecture Notes – Phys 395 Electronics Book

  • Chapter 2Alternating Current CircuitsWe now consider circuits where the currents and voltages may vary with time (V = V (t),I = I(t)(also Q = Q(t))). These lectures will concentrate on the special case in which thesignals are periodic, with time average values of zero ( v(t) = i(t) = 0). Circuits withthese signals are referred to as alternating current (AC) circuits. In general signals will haveboth DC and AC properties (v(t)= VAC(t)+ VDC). We will concentrate only on the ACcomponents and assume that the DC properties can be treated separately using the methodsof the previous lectures.The algebraic equations representing Kirchoff’s laws for DC circuits will take the formof differential equations for AC circuits. So now is a good time to review your differentialequations and complex number theory because we will use it.2.1AC Circuit ElementsIn physical terms, EMFs can be regarded as circuit elements which put energy into a circuitand a resistor R as an element which removes energy from a circuit. The energy is dissipatedin the resistor as heat. In AC circuits we have the additional circuit elements, capacitance Cand inductance L, which store energy in electric and magnetic fields respectively. C and Lare referred to as reactive elements while R is a resistive element. All three of these elementare considered passive elements. We will encounter active circuit elements in the lecturesto follow. For simplicity we will ignore radiation that might be emitted by high frequencycircuits.2.1.1CapacitanceThe fundamental property of a capacitor is that it can store charge and hence electric fieldenergy. The capacitance C between two appropriate surfaces is defined byV =QC,(2.1)where V is the potential difference between the surfaces and Q is the magnitude of the chargedistributed on either surface.21