# The Time Constant Of A First Order System

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Objective The objective of this lab is to firstly evaluate the time constant of a first order system (RC circuit) and to understand its influence on the output at increasing frequencies. The secondary objectives of this lab include observation of the effect of capacitance on the time constant and also the evaluation of the system’s bandwidth. Background A first order system is made up of two major components: an energy-storing component (mass, capacitor, etc.) and an energy-dissipating component (damper, resistor, etc.). The most important consequence of the energy-storing element is the introduction of lag into the system. Figure 1 is an example of a typical first order RC (Resistor and Capacitor) circuit connected to DC battery.…show more content…
A is the cross-sectional area of the plates in square meters, and D is the distance between the plates in meters. When current flows through the wires of the circuit and reaches the capacitor, the capacitor essentially “blocks” the current flow. Positive charge gets collected on one side of the capacitor, and negative charge gets collected on the other side of the capacitor. The two plates are oppositely charged and thus produce a voltage. Capacitors build up voltage quickly when they are uncharged due to the relatively high current flow. Subsequently, the capacitors accumulate voltage slower as they gather more and more electrons. The capacitance of the capacitor and the current supply are the two major factors that determine the time it takes for the capacitor to completely charge. Ohm’s Law V=IR , states that current, voltage and resistance are all linearly related to each other. The current flowing through the circuit can be regulated by modifying the resistance of the circuit. In order to understand and manipulate how long a capacitor will take to charge completely, it is important to understand the concept of time constants. The time constant of a system, measured in seconds, is dependent on its reactive components such as the capacitor or inductor. When a resistor is connected to a capacitor in parallel (RC circuit) the capacitor charges across the resistor till the voltage is equal to the input voltage; This is known as the transient response. After