21.6 DC Circuits Containing Resistors and Capacitors When you use a flash camera, it takes a few seconds to charge the capacitor that powers the flash. The light flash discharges the capacitor in a tiny fraction of a second. Why does charging take longer than discharging? This question and a number of other phenomena that involve charging and discharging capacitors are discussed in this module. RC Circuits An RC circuit is one containing a resistor R and a capacitor C. The capacitor is an electrical component that stores electric charge. Figure 21.38 shows a simple RC circuit that employs a DC (direct current) voltage source. The capacitor is initially uncharged. As soon as the switch is closed, current flows to and from the initially uncharged capacitor. As charge increases on the capacitor plates, there is increasing opposition to the flow of charge by the repulsion of like charges on each plate. In terms of voltage, this is because voltage across the capacitor is given by Ve = QIC, where Q is the amount of charge stored on each plate and C is the capacitance. This voltage opposes the battery, growing from zero to the maximum emf when fully charged. The current thus decreases from its initial value of 1o = emf to zero as the voltage on the capacitor reaches the same value as the emf. When there is no current, there is no IR drop, and so the voltage on the capacitor must then equal the emf of the voltage source. This can also be explained with Kirchhoff's second rule (the loop rule), discussed in Kirchhoff's Rules, which says that the algebraic sum of changes in potential around any closed loop must be zero. The initial current is Io = emt, because all of the IR drop is in the resistance. Therefore, the smaller the resistance, the faster a given capacitor will be charged. Note that the internal resistance of the voltage source is included in R , as are the resistances of the capacitor and the connecting wires. In the flash camera scenario above, when the batteries powering the camera begin to wear out, their internal resistance rises, reducing the current and lengthening the time it takes to get ready for the next flash. Von capacitor 0.632E Switch O r= RC 21 3r 4t (a) (b) Figure 21.38 (a) An RC circuit with an initially uncharged capacitor. Current flows in the direction shown (opposite of electron flow) as soon as the switch is closed. Mutual repulsion of like charges in the capacitor progressively slows the flow as the capacitor is charged, stopping the current when the capacitor is fully charged and Q = C· emf . (b) A graph of voltage across the capacitor versus time, with the switch closing at time t = 0. (Note that in the two parts of the figure, the capital script E stands for emf, q stands for the charge stored on the capacitor, and r is the RC time constant.)