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# LCR - Inductor(L Capacitor(C Resistor(R Circuit(LCR Notes...

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Inductor (L), Capacitor (C), Resistor (R) Circuit (LCR) Notes by Bernd A. Berg Department of Physics Florida State University Tallahassee, FL 32306, USA. (Version March 6, 2011) Copyright c by the author.

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Chapter 1 1.1 LCR circuit We consider a resistor ( R ), a capacitor ( C ) and an inductor ( L ) in series, see figure 1.1. Charge conservation implies I R = I C = I L = I (1.1) where I R , I C and I L are the currents at the resistor, capacitor and inductor, respectively. Figure 1.1: Series LCR circuit with an ac generator. The voltages are related to the currents by the following equations V R = R I and V C = Q C with dQ dt = I (1.2) 1
CHAPTER 1. 2 where Q ( t ) is the charge on the capacitor. As inductor we consider an idealized solenoid (i.e., we neglect boundary effects which distinguish a real solenoid from an infinitely long one). The induced (back) electromotive force (voltage over the inductor) is the derivative of the magnetic flux back = V L = 1 c d Φ m dt = L dI dt (1.3) where the constant L > 0 is called self inductance of the coil. In accordance with Lenz’s law the induced electromotive back will work against the electromotive force emf which drives the circuit. We use complex calculus and the physical quantities are given by the real parts.

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LCR - Inductor(L Capacitor(C Resistor(R Circuit(LCR Notes...

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