Question

(This has to do with Physics)

6.1.1 How does a capacitor charge?

  

6.1.2 How does a capacitor discharge?

   

6.1.3 What is the time constant?

   

6.1.4 What are the units to τ?

Answer 1

A Capacitor is a passive device that stores the energy in its Electric Field and returns energy to the circuit whenever required. A Capacitor consists of two Conducting Plates which are separated by an Insulating Material or Dielectric. When a Capacitor is connected to a circuit with Direct Current (DC) source, two processes takes place, which are called "charging" and "discharging" of the Capacitor.

a) When Capacitor is connected to the DC Power Supply, Current flows through the circuit and both Plates get the equal and opposite charges. The increasing Potential Difference, v_c, is created while the Capacitor is charging. Once the Voltage at the terminals of the Capacitor, v_c, is equal to the Power Supply Voltage, v_c = V, the Capacitor is fully charged and the Current stops flowing through the circuit, the Charging Phase is over. A Capacitor is equivalent to an Open-Circuit to Direct Current, R = ∞, because once the Charging Phase has finished, no more Current flows through it. The Voltage v_c on a Capacitor cannot change abruptly.

b) When the Capacitor is disconnected from the Power Supply, the Capacitor discharges through the Resistor in circuit and the Voltage between the Plates drops down gradually to zero, v_c = 0.

c) The product of Resistance R and Capacitance C is called the Time Constant τ, which characterizes the rate of charging and discharging of a Capacitor. The smaller the Resistance or the Capacitance, the smaller the Time Constant, the faster the charging and the discharging rate of the Capacitor, and vice versa.

d) The time constant (denoted as tau) has the units of time, i.e. seconds.