CHAPTER 2. ALTERNATING CURRENT CIRCUITS22In terms of current, I = dQ/dt impliesdVdt=1CdQdt=IC.(2.2)In electronics we take I = ID (displacement current). In other words, the current ﬂow-ing from or to the capacitor is taken to be equal to the displacement current through thecapacitor. You should be able to show that capacitors add linearly when placed in parallel.There are four principle functions of a capacitor in a circuit.1. Since Q and E can be stored a capacitor can be used as a (non-ideal) source of I andV .2. Since a capacitor passes AC current but not DC current it can be used to connectparts of a circuit that must operate at diﬀerent DC voltage levels.3. A capacitor and resistor in series will limit current and hence smooth sharp edges involtage signals.4. Charging or discharging a capacitor with a constant current results in the capacitorhaving a voltage signal with a constant slope, ie. dV /dt = I/C = constant if I is aconstant.Some capacitors (electrolytic) are asymmetric devices with a polarity that must behooked-up in a deﬁnite way. You will learn this in the lab. The SI unit for capacitanceis farad (F). The capacitance in a circuit is typically measured in µF or pF. Non-ideal cir-cuits will have stray capacitance, leakage currents and inductive coupling at high frequency.Although important in real circuit design we will slip over these nasties at this point.Capacitors can be obtained in various tolerance ratings from±20% to±0.5%.Because of dimensional changes, capacitors have a high temperature dependenceof capacitance. A capacitor does not hold a charge indeﬁnitely because the dielec-tric is never a perfect insulator. Capacitors are rated for leakage, the conductionthrough the dielectric, by the leakage resistance-capacitance product in MΩ· µF.High temperature increases leakage.2.1.2InductanceFaraday’s law applied to an inductor states that a changing current induces a back EMFthat opposes the change. OrV = VA− VB = LdIdt.(2.3)Where V is the voltage across the inductor and L is the inductance measured in henry (H).The more common units encountered in circuits are µH and mH.The inductance will tend to smooth sudden changes in current just as the capacitancesmoothes sudden changes in voltage. Of course, if the current is constant there will be no