 Let's solve a few problems on electric power. Here's the first one. In a closed circuit, a charge of 24 coulombs flows from one terminal of the battery to the other over a duration of one minute. The battery maintains a potential difference v equals 5 volt in the circuit. What is the power input in the circuit? Okay, the first thing I do is just draw a circuit. So here we go. So we are given that we have a battery of 5 volt. There must be some resistor. There must be some current. I don't know what the current is. But we are asked to calculate the power input. What is the meaning of power? Well, power is basically how much energy is being provided per second. And how do you calculate power? Well, the formula for power is equal to v into i. What does this mean? Well, if you take the voltage of the battery and multiply it by the current that the battery is sending, then you will get how much battery, how much power the battery is inputting into the circuit. And similarly, if you multiply the voltage across the resistor with the current through the resistor, you will get how much power is dissipated in the resistor. Now, of course, because of Ohm's law for resistors, you can also write power dissipated as i square r or v square over r. It comes from here only. If you apply Ohm's law, you'll get this. Okay, now what is asked for us, we are asked to calculate how much is the power input in the circuit? So how much is the power that battery delivering to the circuit? That's what we want to figure out. So what do I know? I know the voltage. So I know v. If I can find out the current, I am done. Then I can do p is equal to v into i. But current is not given. Instead, what is given to me is the charge that is going through the circuit in one minute. Now, I know the current is equal to q divided by t. I know that. And so from this, I can calculate the current. q is the charge. These are time I can calculate the current. And once I know the current, I can calculate the power dissipate power input. So why don't you pause the video and see if you can try this on your own first? Okay, so let's do it. So since current is equal to q over t, I know the charges 24 coulombs. And the time taken is one minute. Now I need to be careful about the units. Minute is not the standard unit. I took a minute to seconds. So one minute is 60 seconds. So this becomes 24 coulombs divided by 60 seconds. And if I simplify this, I'll get 0.4 amperes. Now that I have the current, I have the voltage, I can use p is equal to v into i. So power is equal to v into i five times 0.4 amperes five times 0.4 is two watt. So that's our answer. The power input in the circuit is two watts. Let's move on to the next question. We have the, we're asked to find the power dissipated in each bulb over here. So let's see, we have two bulbs that are connected like this. And if they're connected across a battery of six volt, we're asked to calculate the power dissipated in each bulb. The first question that comes to my mind is it's also, what is this 10 volt, 25 watt, 10 volt, 50 watt, wait, power is already given to me, right? Then why are they asking me to calculate power again? Well, this is not how much power is dissipated in the bulb. This is called the rating of the bulb. What it means is that if there was 10 volt that is coming across the bulb, then there would be 25 watt dissipated. It's not saying that right now in this circuit, 25 watt is dissipated because we don't know how much the voltage is. Clearly the voltage has to be less than 10 volt because the voltage of the battery only is six volt. So it's not going to be this. So the rating is given to me, but how do I use this to calculate the power? Well, whenever rating is given, the first thing I do is I calculate the resistance of that bulb because once I calculate the resistance of the bulb, then I can use the power formula and either I can use i square r or v square over r. So the first thing is to calculate the resistance of this bulb using the power ratings and then we can calculate the power dissipated. Okay. Now, how do I calculate the resistance of this bulb? Let's say, well, I know that if 10 volts were to come across it, 25 watt will be dissipated. So I know the voltage and I know the power. So for this rating, can I calculate the resistance? Yes, I can use p is equal to v square over r. So let me do that. So if p is equal to v square over r, r is equal to v square over p. So the resistance of the first bulb will be v square, which is 10 square over p, which is 25 and that gives me 100 by 25. That gives me four. So the resistance of the first bulb is four ohm. Similarly, what is the resistance of the second bulb? Well, the resistance of the second bulb will be v square over r. So 10 square divided by r, which is sorry, v square over p, 10 square divided by 50, which means 100 by 50, which is two ohms. Okay. Now I know the resistor here and resistance here. Let me just write that down. So this is four ohms and this is two ohms, which means I have two resistances connected in a circuit. All right. So if I combine these two, there are two resistance in series. That means the total resistance will be just six ohms. So this is the equivalent circuit. I have a six ohms resistance in this circuit. And since the voltage is six volt, can I calculate the current in the circuit? Yes, we can. And once I calculate the current, that current will be the same over here and therefore I can then calculate what the power is. So why don't you pause the video and see if you can try to do the rest of the work yourself. All right. Let's see. So from Ohm's law, v is equal to i r. So if v is six volt and r is six ohm, we can do this in our head. i should be one ampere, right? Because v is equal to i r. So i is equal to v by r. v by r is six by six is one ampere. So the current over here will be one ampere, which means the current over here will also be one ampere. So I now know the current through this bulb is one ampere. And I also know the resistance of this bulb, four ohms. So I can use p is equal to i square r and solve for power here. And similarly I can solve for power here again. So pause the video and see if you can try the rest of it yourself, if you haven't already. But anyways, let's do it now. So what is the power dissipating the first bulb? It's going to be i square r. It's going to be one square because the current is one and r is four ohms. So one into four, four watt. What will be the power dissipated over here? Well p2 will be again i square r. It's one square times two, two ohms. And that gives me power is equal to two watts. And there we go. We have found the power dissipated in each bulb. This now takes us to the last question. We are given a 100 watt light bulb is used four hours daily for 30 days. The price of electricity is rupees five per unit. What is the cost of consumption? Okay, let's understand what's given to us. We are given a light bulb is used for some time and we're given the price of electricity is rupees five per unit. What is the meaning of the word unit over here? So the commercial unit, it always means kilo watt hour. It's the unit of energy. But what does it mean? Let's quickly understand this. So remember power is equal to energy per time, power how much energy is dissipated or how much energy is consumed per time or how much energy is consumed per second. So from this, what will be energy? Energy will be power into time, right? Now usually the energy unit is in joules, right? But joule is a very small unit. So instead what we do is we come up with a new unit. So in this new unit, what we do is we take the power in terms of kilowatts, not watts, but kilowatts and time in terms of hours, not seconds. So when you do that, the energy that you get is in kilowatt hour. This is what we call one unit. Okay, so now that we know what a unit is, all I have to calculate is how much energy is consumed in terms of kilowatt hours. And then since I know how much is the price of electricity per unit, I can then figure out how much the total prices. So again, why don't you pause the video and see if you can try the rest of it yourself first. All right, so let's see. So I need to calculate the total energy consumed by this bulb. So how do I do that? Well, again, energy is equal to power into time. I know the power is 100 watt. And what is the time? Well, I'm using it for four hours for 30 days. Since I'm using it for four hours every 30 days, so total time will be four into 30 hours. Each day, four hours, 30 days, four into 30 hours. So this is the total energy. Now, I don't, I won't multiply it directly because I need my unit to be kilowatt hour. The time is in hours, so that's perfect. But I want this to be in kilowatts. How do I convert that to kilowatt? Kilowat means thousand. Since I know kilo means thousand, what I'll first do is I'll multiply by thousand and divide by thousand. I'll keep this as it is. Now this number is kilo. So I'll call this as kilo. Let me see. So 100 watt into kilo, everything else is the same. And now I have kilowatt. So now I can simplify. 100 by 1000 is 0.1. So this is 0.1 kilowatt into this is 120 hour. Now, if I multiply this, I get energy as 12 kilowatt hour. So that means I have consumed 12 units. This bulb has consumed 12 units of energy. And since I know for each unit of energy consumed, I have to pay five rupees for 12 units. How much do I have to pay? Well, the price of electricity will be 12 times 5 rupees per unit. And therefore, the total price would be 60 rupees. That's it. That's the answer.