2.2.3 LC Circuit

Chapter 2.2.3 LC Circuit

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

  • CHAPTER 2. ALTERNATING CURRENT CIRCUITS26If a battery is inserted into the circuit the current raises quickly from zero to some finitevalue. The EMF generated in the inductor impedes the current flow until it is constant.The expression for the current in the RL circuit isi(t)=VBR(1− e−tR/L)(2.14)where the time constant is nowτ =LR.(2.15)The voltage across the resistor is an increasing exponential unlike the RC circuit inwhich the voltage across the resistor decreased exponentially. Likewise, the voltage acrossthe inductor decreases with time while in the RC circuit the voltage across the capacitorincreased with time.There are other initial conditions we could work with in this circuit but these can nowbe worked out by the student.2.2.3LC CircuitLets now consider the LC circuit in figure 2.3 which has no resistive element.CLFigure 2.3: LC circuit.Kirchoff’s voltage law applied to the loop isVL + VC =0.(2.16)Substituting our previous expressions for VL and VC givesLdIdt+QC=0.(2.17)Using I = dQ/dt givesLd2Qdt2+QC=0.(2.18)The circuit equation is second-order in Q and one possible solution isQ(t)= Q0 cos(ωt + φ),(2.19)