6.3 THE RLC CIRCUIT In this section we consider the RLC circuit, shown schematically in Figure 6.3.1. As we'll see, the RLC circuit is an electrical analog of a spring-mass system with damping. Nothing happens while the switch is open (dashed line). When the switch is closed (solid line) we say that the circuit is closed. Differences in electrical potential in a closed circuit cause current to flow in the circuit. The battery or generator in Figure 6.3.1 creates a difference in electrical potential E = E(1) between its two terminals, which we've marked arbitrarily as positive and negative. (We could just as well interchange the markings.) We'll say that E (t) > 0 if the potential at the positive terminal is greater than the potential at the negative terminal, E (t) < 0 if the potential at the positive terminal is less than the potential at the negative terminal, and E(t) = 0 if the potential is the same at the two terminals. We call E the impressed voltage. Resistor (Resistance R) www Induction Coil (Inductance L) 00000 Switch Battery or Generator (Impressed Voltage E=E(t)) Figure 6.3.1 An RLC circuit Capacitor (Capacitance C) At any time t, the same current flows in all points of the circuit. We denote current by I = 1(t). We say that I(1) > 0 if the direction of flow is around the circuit from the positive terminal of the battery or generator back to the negative terminal, as indicated by the arrows in Figure 6.3.1 1(t) < 0 if the flow is in the opposite direction, and I(t) = 0 if no current flows at time 1.

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