In the last lecture we had discussion on electric potential difference or voltage and in this lecture we will understand what is electric power and how to determine the sign of electric power or you can say the nature of electric power whether it is getting absorbed or it is getting delivered and we will begin our discussion with the definition of electric power and this definition you will become more clear after some time. So according to the definition of electric power, the amount of electrical energy in the previous lecture we had discussion on the electrical potential energy. So the amount of electrical energy transferred per unit time by an electrical circuit or electrical element is known as electric power. So in simple words we can say that electric power is the time rate of change of electrical energy.
Now to get the clear picture that why we are defining electric power like this, I have taken one very simple case. And after analyzing this case, the definition of electric power will become more clear. And apart from that, we will also get the mathematical formula to calculate the electric power.
Therefore, The analysis is very important and it is very simple at the same time. In this case I have taken the most basic circuit element that is the resistance. And you can see the voltage across the resistance is equal to V volts or you can say the potential difference across the resistance is equal to V volts.
And we know the potential difference is the difference in the electric potentials of two points. And in this case the potential difference V is the difference in the electric potentials of these two points. Let's say the electric potential at this point or terminal is equal to V1 and the electric potential at this point or terminal is equal to V2. And you can notice that this terminal is having the positive polarity and this terminal is having the negative polarity.
And in the previous lecture, I told you the positive polarity means v1 is that the higher potential as compared to v2 and therefore the potential difference we are getting v volts is equal to v1 minus v2 because higher potential minus the lower potential is equal to the given potential difference. And using this we can evaluate some other important parameters. in this particular case. Now apart from the potential difference the direction of current is also given. The current is moving from left to right and therefore the current is entering the positive terminal and the current is leaving the negative terminal.
And it is important to understand what is happening inside this because to get the clear idea of this definition And to get the mathematical formula of power, we must understand what is happening inside this. And we know the direction of current is same as the direction of positive charge movement. And the direction of current is opposite to the movement of negative charge or more precisely electrons.
So in this scenario positive charges are moving in this direction and the negative Charges or electrons are moving in this direction. Now to get the clear idea and to avoid any confusion we will consider the positive charge movement. We will not consider the negative charge movement. However the current in a circuit is mainly due to the movement of electrons and not positive charge movement.
But for simplicity we will consider the movement of positive charge. You can also consider the movement of negative charge. But in that scenario you have to be careful about the negative signs. So let's begin our analysis considering the positive charge movement.
And in this scenario the positive charges we are having are moving from higher potential point to the lower potential point. Now what will happen to the electric potential energy in this scenario when positive charges are moving from higher potential point to the lower potential point. To the lower potential point what will happen to the electric potential energy?
Let's say the electric potential energy has This terminal is equal to U1 and in the previous lecture we saw the electric potential energy is equal to the charge multiplied to the point's potential and here the potential of this point is equal to V1 and let's say the charge moving from higher potential to lower potential is equal to Q. So multiplying Q and V1 we will have U1. Similarly we can have The electric potential energy at this terminal for this we are required to multiply Q with V2.
Now we know V1 is greater than V2. This means QV1 will also be greater than QV2. And this clearly indicates when we are moving from positive terminal to negative terminal there is decrement. in the electric potential energy.
U1 was higher as compared to U2. U1 is higher as compared to U2 and while moving from high potential to low potential the energy is becoming U1 to U2. This means we are losing the electric potential energy somewhere and the amount of electric potential energy lost is represented by delta U.
And it is equal to u1 minus u2 and we can write this as qv1 minus qv2 qv1 minus qv2 or we can write q inside the bracket v1 minus v2. Now v1 minus v2 is the potential difference v. So we can write the energy lost while moving from positive terminal to the negative terminal equal to Q multiplied to the voltage V. And this is how we can understand that electrical energy is transferred per unit time. The electrical energy is getting reduced. This means it is getting transferred and now we will try to understand in what form it is getting converted. And the first thing which comes in our mind that this amount of electrical potential energy is getting converted to the kinetic energy.
This means this amount of potential energy is getting converted to the kinetic energy and hence increasing the overall kinetic energy of the charges. So charges will have somewhat lower kinetic energy before entering the positive terminal and after some time their kinetic energy will increase moving through the resistor and finally they will leave with a higher kinetic energy. This means current before entering the resistor will be lower as compared to the current after leaving the resistor which is not at all true. The current will remain same and therefore we cannot say that this amount of potential energy is getting converted to the kinetic energy.
So where this energy? is going. We know the resistance will have the atoms and molecules and when the positive charges we are having enter the resistance and move towards the negative potential they will collide with the atoms and molecules present in the resistor and therefore the atoms and molecules will now vibrate at higher frequency and due to this vibration heat will be produced and when you touch the resistor you will find it is heated. So, we can say that the reduced electrical potential energy is getting converted to the thermal energy in the resistor.
So this is where the energy is going and therefore to calculate the energy transferred we can focus on the definition of power because we know there is very close relation between work and energy. Power is equal to work. per unit time and we know change in energy is equal to work. So we can write power is equal to energy per unit time and in our case the energy is equal to delta u because this amount of electrical potential energy is getting converted to the thermal energy and we are calculating the thermal energy or you can say the energy gained by the resistor.
So in place of E I will write delta U. So the power is now equal to delta U divided by D. Delta U is equal to Q multiplied to voltage V. So, power is now equal to Q multiplied to voltage V divided by T.
And we know charge per unit time, that means Q divided by T is equal to the current in the circuit and current is equal to I. Therefore, we can say that the power which is the electric power is equal to current I multiplied to V. So, remember. This because we will calculate the electric power using this.
Now we will focus on the nature of the power and this is very important and confusing. Therefore we will try to get the simple conclusion so that we can solve the questions without making any error. In this case you can see power is positive.
We are having positive sign and this is happening when the current I is entering the positive terminal. and it is leaving the negative terminal and we know the resistor is absorbing the power. So when p is equal to plus iv this means the element we are having is absorbing the power or you can say the element is acting like a sink. And now I will conclude it whenever the current enters the positive terminal the power is absorbed in this case you can see current is entering the positive terminal and the resistor is absorbing the power and the sign of the power is positive or you can write power is equal to plus IV so remember this point whenever current is entering the positive terminal of any circuit element I have taken one black box to represent the circuit element It does not matter what is inside this. The only thing matters is the polarity of the voltage and the direction of the current.
If current is entering the positive terminal or leaving the negative terminal then the power will be positive and the element will absorb the power or you can say it will act as sink. Now we will move on to the next point. When the current leaves the positive terminal, power is delivered. In this case you can see that the current is leaving the positive terminal or you can say the current is entering the negative terminal. The power is delivered and the sign of the power will be negative.
So we have minus i multiplied to v and as the power is delivered this element is acting as the source. So remember this point. Now there is one more way to think about it. Whenever the current is entering any terminal then the sign of that terminal will be the sign of the power. Like in this case current is entering the positive terminal so positive sign will be there for the power and in this case current is entering the negative terminal so negative sign will be there for the power.
So remember all these points and they are very helpful while solving the questions. Now we will move on to some examples to practice what we have learned till now. But before that I want to tell you one more point.
Here power is equal to minus IV. This means this particular element is acting as the source in the circuit. But you can also consider it as a load and in that scenario the power minus IV will get absorbed by the element. Now we will move on to the examples.
In the first example we are having current i entering the positive terminal of this element having the voltage v. Then we know the power is equal to plus i v and the element will act as sink or you can say it will act as load. And in the second case you can see current is leaving. the positive terminal or you can say current is entering the negative terminal and if the voltage is v then the power will be minus iv and in this scenario this element is acting as the source and now we will understand the third example and the third example is little bit tricky this example is tricky because when you calculate the power first you will get the wrong answer. Let's calculate the power and see why we are getting the wrong answer. You can see current is having this direction.
This means current I is entering the positive terminal and if the voltage is equal to V then we will get power equal to plus I V which is not correct. This power is incorrect. Let's understand why this power is incorrect and for that we will use the example number one. In this example Current is entering the positive terminal from the outside But inside when you look closely you will find the same current is moving from positive Terminal to the negative terminal so inside when current enters the negative terminal power is going to be positive similarly when current Inside enters the positive terminal the power is negative now in this case you can see Positive terminal is this one, negative terminal is this one and current inside is entering the positive terminal. Therefore, power will be negative and it will be equal to minus IV and therefore the element will act as source.
Let's move on to the fourth and the last example. In this case, current is entering the negative terminal inside. And if the voltage is equal to V then the power will be equal to plus IV and the element we lacked as sink.
So this is all for the examples and now we will move on to the homework problem. In the homework problem we have one element and the potential difference or the voltage across the element is equal to 8 volts and you can see the polarity. The current is entering to the negative terminal and the current is equal to 2 amperes. Now it is your task to calculate the power along with the proper sign and also tell me whether the element is acting as source or sink. So this is all for this lecture.
See you in the next one.