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Why capacitor doesn’t allow sudden change in the voltage – In depth analysis


Why capacitor doesn’t allow sudden change in the voltage – In depth analysis

In our studies we come through the capacitors and its usages in many applications. Almost 90 percent of the students don’t know why the capacitor does not allow the sudden changes in the voltage. But still they are trying to plot graphs of the experiment in laboratory. Consider an example RC low pass filter circuit experiment in circuit’s laboratory, when a square wave is applied to the RC low pass filter the output of the circuit is exponential rise towards the maximum voltage during positive square pulse input and for the negative input the output rises exponential towards the negative voltage.

In such circuit, for sudden rise of input voltage from zero to maximum the capacitor voltage is exponential rise towards the maximum voltage. At that time our lectures or tutors will say “capacitor doesn’t allow sudden changes in the voltage”. Then a question arises in our mind why the capacitor doesn’t allow sudden changes in the voltages?.

Before going to know about the answer for the above question let us look for the simple basics of capacitor. Off course we can write a complete text book about capacitors, but here the discussion is limited.


What is a capacitor?

A capacitor is an electronic device has the capability to store electric energy by holding electric charge.

How Electric charged is stored in the capacitor?

The basic model of the capacitor contains two conducting materials separated by an insulating material or vacuum. For the simplicity, we assume two parallel plates as conducting materials separated by vacuum as shown in fig 1.1.

  Figure 1.1 Two parallel plates with vacuum as dielectric create a capacitor. 

Formula for capacitance is given by (C) = Charge (Q)/Voltage (V)

V: Potential difference between two conductors.
Q: Magnitude is charge on one of the conductors.
C: Capacitance in farads

1 Farad = 1 Columb/1Volt

When a battery is connected to a parallel plate capacitor as shown in the figure 1.2, the capacitor starts charging towards the maximum voltage of battery. Assume initially the capacitor has no charge that means both plates are neutral (each plate have equal number of protons and electrons). If a battery is connected to a parallel plate capacitor, the positive terminal of the battery forcibly attracts the electrons from the capacitor plate A and the negative terminal of the battery will send the electrons to capacitor plate B. Therefore the plate A becomes more positive and plate B becomes more negative.

Figure 1.2 A battery is connected to a capacitor to make it charge. 
The number of electrons that are accumulate on plate B is equal to the number of electrons that are attracted by the positive terminal of the battery from plate A. In this way the plates of the capacitor will get charged as positive and negative and this charging process will continue until the voltage across the capacitor reaches maximum voltage of the battery. This charge stored in a capacitor will not go anywhere until you provide a discharge path. Simple discharge path to a capacitor is just short circuit the two terminals of the capacitor.

 Caution: Does not touch the charged capacitor lead with your hands which may cause shock and it may be worse when the capacitor is large.



Why capacitor doesn’t allow sudden change in the voltage

Here the solution is explained by taking four different cases. For better understanding only two electrons movement is shown and also the time taken to move the electrons is shown in seconds. But remember practically millions of electrons will flow in fraction of seconds.

Case 1 (t = 0): At t = 0, the switch is opened therefore there is no charge flow. That means the capacitors plates are neutral and the potential difference across the capacitor is zero. Therefore the voltage across the capacitor is zero.

Case 2 (t = t1): Whenever the switch is closed (sudden change in voltage from 0V to 5V), the positive terminal of the battery will attract electrons from the plate A and at the same time the negative terminal of the battery will provide same number electrons to plate B in very small amount of time. Therefore the voltage rises linearly towards the maximum voltage as shown in the voltage graph. But current graph is initially is at its maximum this is because the number of electrons passing in given time is defined as current (I = Q/T). If the time is short, obviously the current is Maximum.

Case 3 (t = t3): The deficiency of electrons on the plate A, make it more positive. Similarly the plate B is more negative due excess of electrons. Because of the more positive charge of the plate A will make the electron movement difficult, hence the movement of electron is slow and the voltage graph is slowly rising and is into curved shaped. The time required to move the electrons towards the positive terminal of battery from plate A is increased, therefore the fall in current is shown in the graph. Similar situation will happen at the negative terminal.
                       
Case 4 (t = t4): Now the plate A is more positive and the plate B is more negative in nature.
Due to this, more time is required to bring the electron from the plate A to the battery positive terminal. Hence the voltage graph is almost parallel to x axis. And the current is almost zero and graph reaches to x axis.


Conclusion: During the capacitor charging the capacitor plates get charged, so that the attraction and repulsive forces of the capacitor plates will make the electron flow difficult. Hence the capacitor will not allow the sudden changes in the voltage.








3 comments :

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3 comments :

Urooj Shah said...

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