Full transcript of “Electric Potential Difference (Voltage)”. Click a timestamp to open the video at that moment. Need another video? Use the YouTube transcript generator.
0:00 in the last lecture we saw why electric current is a scalar quantity and in this lecture we will understand what is electric potential what is electric potential energy what is electric potential difference all voltage and some other important points and I will begin with defining electric potential difference or voltage electric potential difference as the name is suggesting is the difference in the electric potentials had two points and it is clear that to understand electric potential difference completely we must understand what is electric potential forced and to understand all these I
0:46 have taken one arrangement and in this arrangement you can see we are having a conducting plate and the conducting plate is having the excess positive charge and therefore there will be electric field and we can visualize electric field graphically using the electric lines of forces and we know the electric lines of forces leave the positive charge and they terminate at the negative charge and therefore you can see electric lines of forces are leaving the positively charged conducting plate and we can define the electric field at a point using a vector
1:35 which is known as electric field strength or we can use a scalar and it is known as electric potential represented by V so we can define the electric field using a vector or a scalar and the vector is known as electric field strength and the scalar is known as electric potential now apart from this plate we have taken one reference point and the reference point is usually located at infinity and we know the influence electric field will be higher near the plate and if we move away from the plate the influence of the electric field will
2:21 reduce therefore if we take one point here and one point here then it is obvious that the influence of electric field will be higher at this point as compared to this point and therefore the electric field strength and the electric potential will be higher at this point and they will be lower at this point now look at the plate and the reference point you will find there is infinite distance between the plate and the reference point and therefore the electric field of this plate will have zero influence at the reference point and now we will take one test charge at the reference point let's say the test
3:07 charge is positive and the charge is equal to Q and we are interested in moving this test charge towards the plate and remember we are moving the test charge towards the plate without accelerating the charge we are not accelerating the charge because we don't want other energies to come into picture and influence the potential energy we are calculating and let's say in this field the charge is at this position and this position is let's say position 1 and if you look closely you will find there is a positive charge plus Q in front of a positively charged
3:55 plate and therefore this plate will repel this charge and we will have a force of repulsion or you can say the electric force repelling this charge in this direction and let's say the forces represented by half a vector and now if we want to move this charge further towards the plate then we need to do some work and this work will get stored in the form of electric potential energy say after doing some work the charge is now at this position let's call it position two and you can see there is some displacement between position 1 and
4:41 position 2 so we have overcome the force and we have displaced the charge to a new position which is position 2 and the work done in moving the charge from position 1 to position 2 is equal to the dot product of force and the displacement and I have already told you the work done in moving the charge from one position to another position will get stored in the form of electric potential energy so this work done will get stored in the form of electric potential energy U and we also know the force is equal to the electric field
5:31 strength multiplied to the charge we are moving so in place of force we can write V vector multiplied to Q therefore the electric potential energy U is equal to e multiplied to Q multiplied to the displacement so you can see one thing the electric potential energy is depending on the charge we are moving in the electric field if we change the charge the electric potential energy will also change so electric potential energy is dependent on the charge we are moving in the electric field on the other hand if we talk about the electric
6:16 potential then it is equal to the work done per unit charge in moving a charge from the reference point to any specific point in the electric field and we know the work done will get stored in the form of electric potential energy therefore electric potential he's also equal to the electric potential energy per unit charge now let's take one example to understand it in a much better way in this example I am considering that we have a test charge which is plus Q and it is moving from the reference point to this particular position which is position 1
7:03 and the potential at position 1 is V 1 and we know the potential at the reference point which is infinity or usually the earth is equal to zero volt so according to the definition of electric potential V 1 V 1 will be equal to the work done in moving plus Q from reference to this position divided by the charge Q let's say work done in moving the charge from reference to position 1 his W infinity to 1 dividing it by the charge we are moving will give us V 1 or we can write this as
7:50 electric potential energy stored while moving from infinity to 1 divided by the charge now we can further write this as u 1 divided by Q minus u infinity divided by Q u 1 is the electric potential energy at position 1 while moving charge Q + u infinity his the electric potential energy at the reference point while moving charge Q now look at this and compare this with this and you will find we are not only calculating V 1 but we are calculating V 1 minus the electric potential at the
8:36 reference point which is equal to zero volt so we are calculating V 1 minus zero volt and this is potential difference this is potential difference because here we are having the difference in the electric ten shares had the two different points v1 his the electric potential at position one and the zero volt is the electric potential at the reference point so we are calculating the difference between the electric potentials had the two different points so we have the potential difference hand it will be equal to v1 only which is the potential at this point so remember this important concept that whenever the potential at the point is given in the
9:23 electric field then it is calculated with respect to the reference point for example let's say v2 is the electric potential at position two then v2 is calculated with respect to the reference point similarly let's say this point is having the electric potential V three then it is also calculated with respect to the reference point and now let's understand why electric potential is the function of position from here we can calculate the potential difference V 2 minus V 1 V 2 minus V 1 and it will be equal to the electric potential energy stored while moving the charge from
10:09 position 1 to 2 from position 1 to 2 divided by the charge itself and this will give us the dot product between the electric field strength and the displacement so you can see that V 2 minus V 1 is independent of the charge we are moving from position 1 to position 2 therefore the electric potential is independent of the charge you are moving it is only dependent on the position each and every point in the electric field will have some potential and it will not depend on the charge you are placing at that particular position but the electric potential energy will depend on the charge for example if you
10:57 place one charge here and this charge is equal to 2 Coulomb then the electric potential energy at this position be equal to two Coulomb multiplied to the potential V 3 this will be the electric potential energy on the other hand the electric potential will only depend on the position it will not depend on the charge you are placing at that particular position this is very important point we will move on to the next point and the next point is related to shifting of the reference point if we shift or change the reference point then the potential difference will not change for example let's say the reference
11:44 point has now shifted to this position with respect to this position the potential at this position will change let's say it is V 1 - similarly potential will change here as well V 2 - then the potential difference V 2 - minus V 1 - who will remain same as V 2 minus V 1 V 2 minus V 1 this is the potential difference so potential difference will never change if you change the reference point this is one very important point and now I will give you the units of electric potential and electric potential energy electric potential energy is having the SI unit has Joule and we know electric potential
12:33 is equal to electric potential energy divided by charge therefore the unit of electric potential is equal to Joule per Coulomb and the unit of electric potential difference will be same as the electric potential Joule per Coulomb or Joule Coulomb inverse all we can use the unit volts for electric potential difference Hall voltage this unit is named after the Italian physicist Alessandro Volta and this is all for electric potential difference electric potential and electric potential energy now we will move on to the next part of the lecture battery
13:20 also known as the voltage source this is known as voltage source because there is potential difference there is potential difference between the positive terminal and the negative terminal let's say the potential difference is 5 volts in this battery this means the potential at the positive terminal minus the potential at the negative terminal is equal to 5 volts let's say the potential at the positive terminal is represented by VP and potential at the negative terminal is represented by V n then VP minus VN is equal to 5 volts and in a battery the
14:06 positive terminal is at the higher potential and the negative terminal is at the lower potential so here we are calculating the higher potential minus the lower potential and we are getting it equal to 5 volt which is the potential difference and we have the conducting wires connected to the positive terminal as well as the negative terminal and if there is no loss in this wire then potential at this end of the wire will be equal to VP and potential at this end of the wire will be equal to VN and we can represent the battery like this as well the longer
14:51 line is representing the positive terminal and the shorter line is representing the negative terminal and again you will have VP minus VN equal to 5 volts this is another representation for the battery because every time making battery like this in a circuit is in not a very efficient way so we replace the battery by this symbol and there is one more symbol which is very frequently used to represent the DC voltage source in this symbol we are having a circle and then we have positive and negative signs positive sign means the terminal is at the high potential and
15:37 negative sign means this terminal is at the low potential so if this voltage source is the voltage source of five volts then let's say this particular point is having the potential v1 this particular point is having the potential V 2 so we always subtract the low potential point from the high potential point this means v1 minus v2 which is high potential minus the low potential and this will give us the potential difference which is 5 volt so whenever you have a voltage source and it is giving you some value then this means it is giving you the potential difference
16:24 between the positive terminal or the high potential terminal and the negative terminal or the low potential terminal now you don't have to worry about this high and low every time I will tell you one easy way to find out the potential difference you simply have to start from one point let's say you start from v1 so write v1 first and then move further and you will encounter with a potential difference which is equal to 5 volt so write 5 and the sign you will have between v1 and 5 will depend on the next to next terminal the next terminal after moving from v1 is the positive terminal
17:11 but we have to focus on next to next terminal which is negative terminal so sign will be negative and then you simply equate the last potential point with this so this is what he will get now rearranging this you will get v1 minus v2 equal to 5 volt which is same as this one or you can start from v2 so let's start from v2 then moving further we can see that there is a potential difference of five volts so I will write five-year and the sign we will have is positive because we have to
17:56 focus on next to next terminal sign which is plus in this case so we have v2 plus five and finally we will equate it with the last or you can say the final points potential which is v1 and rearranging this we will have v1 minus v2 equal to five volts which is same as this one and now we will move on to the last point in this lecture according to this point if you place negative sign in front of the potential difference then the polarity will reverse like in case of electric current we saw negative sign reverse the direction of the current similarly negative sign in case of
18:42 potential difference will reverse the polarity for example if we place negative sign in this case and we have minus 5 volts instead of 5 volts then the polarity will reverse like this instead of plus we have minus and instead of minus we will have plus so this is another important point and if you compare the first two cases with the last two cases you will find there is difference in the representation of the connecting wires in the first two cases the wires are drawn without any tension kind of relaxed but in the last two cases the wires are not at all relaxed
19:28 but tense and this is how you will find the networks drawn in the books therefore from now on we will draw wires like this so this is all for this lecture and in the next lecture we will talk about electric power [Applause] [Music]
