25 RC Circuits: Voltage and Current Analysis in Circuits Containing Resistors and Capacitors in Series
25.1 Introduction
In this chapter, we will examine the concepts behind resistor–capacitor series circuits, known as RC circuits.
As explained in previous chapters, when a voltage is applied to a completely discharged capacitor, it makes the capacitor charge exponentially to the power supply voltage. As it happens, current will decrease, also exponentially, to 0.
25.2 Charging a Capacitor
Consider the circuit shown on Figure 25.1, composed of a resistor and a capacitor in series with a switch and a power supply. The switch is initially open, so the circuit is not working. The capacitor is completely discharged.
Figure 25.1 RC circuit and an open switch.
At time t = 0 s, the switch is closed. Current starts flowing from the power supply through the resistor R and reaches the capacitor. The capacitor starts to charge.
Current is at its maximum value, just limited by the resistor. As charging starts, the capacitor is seen, by the circuit, as a wire, a short circuit, because it makes no opposition to the current flow.
As time passes and the capacitor charges, current will exponentially decrease to 0, and voltage across the capacitor exponentially increases to the power supply voltage. Variations of current and voltage will then stop and the circuit will stabilize.
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