2.2.1 RC Circuit

Chapter 2.2.1 RC Circuit

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

  • CHAPTER 2. ALTERNATING CURRENT CIRCUITS24We will first consider the transient response. This will be one of the few times we considernon-oscillating AC behaviour. Since Ohm’s law and Kirchoff’s laws are linear we can usecomplex exponential signals and take real or imaginary parts in the end. This is not truefor power, since it is non-linear (product of signals).2.2.1RC CircuitConsider the resistor R and capacitance C in the circuit loop in figure 2.1. Notice that thereis no source.CRFigure 2.1: RC circuit.We start with a differential version of Kirchoff’s voltage law.ddtiVi =idVidt=0.(2.5)When applied to our circuitdVCdt+dVRdt=0,(2.6)where VC is the voltage drop across the capacitor and VR is the voltage drop across theresistor.The change in the voltage drop across the capacitor is given by our previous expression,dVCdt=IC.(2.7)The change in the voltage drop across the resistor can be obtained from Ohm’s lawVR = RI⇒dVRdt= RdIdt.(2.8)Substituting these changes in voltage into Kirchoff’s equation givesIC+ RdIdt=0,(2.9)where the current due to the flow of charge on or off the capacitor is the same as throughthe resistor.Now we need some initial conditions. Notice that although the capacitor behaves as anopen circuit to DC, current must flow to charge or discharge the capacitor. Lets take the