Download Inductors and Capacitors: Understanding Energy Storage and Power in Electrical Circuits and more Study notes Electrical Circuit Analysis in PDF only on Docsity! 6-1 6. Inductance and Capacitance, and Mutual Inductance Two new circuit elements Inductor An inductor is an electrical component that opposes any change in electrical current. It is composed of a coil of wire wound around a supporting core. An inductor can store energy. Capacitor A capacitor is an electrical component that consists of two conductors separated by an insulator or dielectric material. A capacitor can store electrical charge. Inductors and capacitors are classified as passive elements and they cannot generate energy. 6.1 Inductor The symbol for impedance is L and measured in henrys [H]. The relationship between the voltage and current at the terminals of an inductor: ∫ += = t t tivd L ti dt diLv 0 )(1)( 0τ • If current is constant, the voltage across the ideal inductor is zero • Current cannot change instantaneously in the inductor 6-2 Example 6.1a For t<0, i(t)=0 For 0<t≤1, tidti t ∫ =+= 0 3 2)0(2 3 1)( τ For 1<t≤2, 1 3 1)1()1( 3 1)( 1 +−=+−= ∫ tidti t τ i(mA)
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Figure 6.8 The variables i, v, p, and w versus ¢ for Example 6.1.
From: Nilsson/Riedel, Electric Circuits, 6e, July 2000 Prentice Hall, Inc.
6-6 Example 6.3 0,20)( 0,0)( 10 >= <= − tVtetv ttv t Find i, p, w. ∫ ∫ = −−== −−=+ − =+= −−− −− − − t ttt tt t t pdw Wetetevip eteedeti 0 101010 1010 0 0 10 10 )]101(2[20 )101(2)]110( 100 [200020 1.0 1)( τ τττ τ τ 6-7 6.2 Capacitor It is represented by C and is measured in farads (F). The relationship between the voltage and current at the terminals of a capacitor: )(1)( 0 0 tvid C tv dt dvCi t t += = ∫ τ The power is: dt dvCvvip == The energy is: 2 2 1 cvw = • A capacitor does not permit an instantaneous change in its terminal voltage. • If voltage is constant, a capacitor behaves as an open circuit. • Only a time-varying voltage can produce a displacement current. i(mA)
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Figure 6.12 The variables i, v, p, and w versus / for Example 6.5.
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From: Nilsson/Riedel, Electric Circuits, 6e, July 2000 Prentice Hall, Inc.
6-11 Example 6.5 ≥ <≤ < = 20 20 00 )( t tt t ti For t<0 0)(1)( == ∫ ∞− t di C tv ττ For 0≤ t<2 4 |) 2 ( 2 1 2 10)(1)0()( 2 0 2 00 ttddi C vtv t tt ==+=+= ∫∫ ττττ For t≥2 10 2 1 4 2)(1)2()( 2 2 2 =+=+= ∫∫ tt ddi C vtv τττ 6-12 6.3 Serial-parallel combination of inductance and capacitance Serial-parallel combination of inductors or capacitors can be reduced to a single inductor and capacitor. Inductor is serial dt diLv LLLL dt diLLLvvvv = ++= ++=++= 321 321321 )( Inductors in parallel Total inductance value )()()()(),111(1 )(1 )()()()111( 0302010 321 0 030201 321 321 0 0 titititi LLLL tivd L i tititivd LLL iiii t t t t ++=++= += +++++=++= ∫ ∫ τ τ
