Thread: Fsc 2nd Year chapter No :1 | ELECTROSTATICS Topic No:16

1. Fsc 2nd Year chapter No :1 | ELECTROSTATICS Topic No:16

Fsc 2nd Year chapter No :1 | ELECTROSTATICS

Topic No:16

CHARGING AND DISCHARGING A CAPACITOR

A Capacitor is a passive device that stores energy in its Electric Field and returns energy to the circuit whenever required. A Capacitor consists of two Conducting Plates separated by an Insulating Material or Dielectric. Figure 1 and Figure 2 are the basic structure and the schematic symbol of the Capacitor respectively.

Figure 1: Basic structure of the Capacitor

Figure 2: Schematic symbol of the Capacitor
When a Capacitor is connected to a circuit with Direct Current (DC) source, two processes, which are called “charging” and “discharging” the Capacitor, will happen in specific conditions.
In Figure 3, the Capacitor is connected to the DC Power Supply and Current flows through the circuit. Both Plates get the equal and opposite charges and an increasing Potential Difference, vc, is created while the Capacitor is charging. Once the Voltage at the terminals of the Capacitor, vc, is equal to the Power Supply Voltage, vc = V, the Capacitor is fully charged and the Current stops flowing through the circuit, the Charging Phase is over.

Figure 3: The Capacitor is Charging
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 vc on a Capacitor cannot change abruptly.
When the Capacitor disconnected from the Power Supply, the Capacitor is discharging through the Resistor RD and the Voltage between the Plates drops down gradually to zero, vc = 0, Figure 4.

Figure 4: The Capacitor is Discharging
In Figures 3 and 4, the Resistances of RC and RD affect the charging rate and the discharging rate of the Capacitor respectively.
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, Figure 5.

Figure 5: The Voltage vc and the Current iC during the Charging Phase and Discharging Phase
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.
Capacitors are found in almost all electronic circuits. They can be used as a fast battery. For example, a Capacitor is a storehouse of energy in photoflash unit that releases the energy quickly during short period of the flash.

PARTS AND MATERIALS

• 6 volt battery
• Two large electrolytic capacitors, 1000 µF minimum (Radio Shack catalog # 272-1019, 272-1032, or equivalent)
• Two 1 kΩ resistors
• One toggle switch, SPST ("Single-Pole, Single-Throw")

Large-value capacitors are required for this experiment to produce time constants slow enough to track with a voltmeter and stopwatch. Be warned that most large capacitors are of the "electrolytic" type, and they are polarity sensitive! One terminal of each capacitor should be marked with a definite polarity sign. Usually capacitors of the size specified have a negative (-) marking or series of negative markings pointing toward the negative terminal. Very large capacitors are often polarity-labeled by a positive (+) marking next to one terminal. Failure to heed proper polarity will almost surely result in capacitor failure, even with a source voltage as low as 6 volts. When electrolytic capacitors fail, they typically explode, spewing caustic chemicals and emitting foul odors. Please, try to avoid this!
I recommend a household light switch for the "SPST toggle switch" specified in the parts list.

CROSS-REFERENCES
Lessons In Electric Circuits, Volume 1, chapter 13: "Capacitors"
Lessons In Electric Circuits, Volume 1, chapter 16: "RC and L/R Time Constants"

LEARNING OBJECTIVES

• Capacitor charging action
• Capacitor discharging action
• Time constant calculation
• Series and parallel capacitance

SCHEMATIC DIAGRAM

ILLUSTRATION

INSTRUCTIONS
Build the "charging" circuit and measure voltage across the capacitor when the switch is closed. Notice how it increases slowly over time, rather than suddenly as would be the case with a resistor. You can "reset" the capacitor back to a voltage of zero by shorting across its terminals with a piece of wire.
The "time constant" (τ) of a resistor capacitor circuit is calculated by taking the circuit resistance and multiplying it by the circuit capacitance. For a 1 kΩ resistor and a 1000 µF capacitor, the time constant should be 1 second. This is the amount of time it takes for the capacitor voltage to increase approximately 63.2% from its present value to its final value: the voltage of the battery.
It is educational to plot the voltage of a charging capacitor over time on a sheet of graph paper, to see how the inverse exponential curve develops. In order to plot the action of this circuit, though, we must find a way of slowing it down. A one-second time constant doesn't provide much time to take voltmeter readings!
We can increase this circuit's time constant two different ways: changing the total circuit resistance, and/or changing the total circuit capacitance. Given a pair of identical resistors and a pair of identical capacitors, experiment with various series and parallel combinations to obtain the slowest charging action. You should already know by now how multiple resistors need to be connected to form a greater total resistance, but what about capacitors? This circuit will demonstrate to you how capacitance changes with series and parallel capacitor connections. Just be sure that you insert the capacitor(s) in the proper direction: with the ends labeled negative (-) electrically "closest" to the battery's negative terminal!
The discharging circuit provides the same kind of changing capacitor voltage, except this time the voltage jumps to full battery voltage when the switch closes and slowly falls when the switch is opened. Experiment once again with different combinations of resistors and capacitors, making sure as always that the capacitor's polarity is correct.

COMPUTER SIMULATION
Schematic with SPICE node numbers:

Netlist (make a text file containing the following text, verbatim):
Capacitor charging circuit v1 1 0 dc 6 r1 1 2 1k c1 2 0 1000u ic=0 .tran 0.1 5 uic .plot tran v(2,0) .end

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