5.1: First-Order Circuits
First-order electrical circuits, which comprise resistors and a single energy storage element - either a capacitor or an inductor, are fundamental to many electronic systems. These circuits are governed by a first-order differential equation that describes the relationship between input and output signals.
One common example of a first-order circuit is the RC (resistor-capacitor) circuit. These circuits are used in relaxation oscillators such as neon lamp oscillator circuits. When voltage is applied to an RC circuit, the capacitor begins charging, and the lamp acts as an open circuit. As the capacitor charges up to the required voltage to ionize the neon gas inside the lamp, the lamp suddenly becomes a short circuit. This causes the capacitor to discharge, creating a flash of light. Once the capacitor discharges fully, the process repeats, leading to a continuous flashing effect.
The time interval between these flashes depends on the time constant of the circuit, which can be adjusted by tuning the resistance (R) and capacitance (C) values. By carefully choosing these values, the frequency of the flashes can be controlled.
In tube lights, a different type of first-order circuit, known as an RL (resistor-inductor) circuit, is utilized. The choke coil in the tube light serves as the inductor, while the inherent resistance of the wire functions as the resistor. Upon voltage application, the choke resists a sudden increase in current, generating an electromotive force (emf) that rises with the applied voltage. This emf ionizes the gas within the tube light, causing it to illuminate.
In an RL circuit, the time constant is defined as the inductance (L) over the resistance (R). This time constant plays a vital role in determining how quickly the circuit responds to changes in the input signal. The larger the time constant, the slower the circuit responds, and vice versa.
