Solved example - Cost of operation of electrical device

an air conditioner has a rating of two kilowatt find the cost of operating it for 10 RS given cost per unit is 3 rupees so let's first write down what we are asked we need to calculate the cost for operating it for 10 hours so let's write it down cost for 10 hours this is what we want now let's see what's given to us an air conditioner has a rating of 2 kilowatts which means we are given the power rating of the air conditioner this is given as 2 kilowatt and we need to calculate the cost for 10 hours which means we are given what is the time for which this is being used 10 ours and we're also given the cost per unit is 3 rupees so let's write that down so we know cost let's use a different color for this so it is cost per unit is 3 rupees so from this data how do we find how much is the cost for 10 hours I think the crucial thing over here is to understand what we mean by this word unit if we understand this and we can solve this easily so in electricity whenever they use the word unit the word unit actually stands for kilowatt hour what do we mean by kilowatt R it's a unit of energy for example if you have a power of 1 kilowatt for any device and if you use that device for 1 R then the energy consumed is by definition 1 kilowatt R but if the device you're using has a power of 2 kilowatts and use it for one R then the energy consumed would be 2 kilowatt hours so that's basically what kilowatt R is you just multiplied the power and time and you get energy that's what energy is all right so now that we know what a kilowatt R is and we know what our power rating is and we know for how long we are using can we calculate how much would be the cost for 10 hours so great idea to pause the video and just think about how we will do it all right so let's do this since we want the cost for 10 hours the first step for us would be to figure out how many units are being used how many kilowatt hours are being used because we know for one kilowatt are the amount is 3 rupees so if we figure out how many kilowatts are is being used we can calculate how many rupees it is so the first step would be to calculate in 10 hours so for 10 hours how many kilowatt our it is well the power is 2 kilowatt the time is 10 hours so how much would be the energy consumed well from this we can clearly say the energy consumed just by looking at the units you can say kilowatt are 2 kilowatt times 10 hours would be so 2 kilowatt times 10 hours that would be 20 kilowatt hours so the energy that is being consumed is 20 units 20 units so in 10 hours 20 units of energy has been consumed now we know for one unit we have to pay 3 rupees so for 20 units how much should we pay well the cost would be 20 times 3 rupees so the cost would be 20 times 3 rupees that's going to be 60 rupees 60 rupees and so there we have it we've solved our first problem let's do one more a bulb of reading 20 watt is used fires every day find the cost of operating it for 30 days given the cost per unit is 4 rupees great idea to pause this video and see if you can try to do this one yourself alright let's do this so again let's find out what's asked we're asked to find the cost of operation so again the same question cost for 30 days this time 30 days and let's see what's given we are given the power rating of the bulb power rating is 20 what we are given it's used 5 hours every day hmm that's going to be important so T is 5 hours per day and it's used for 30 days so it's used for 30 days this is going to be important and we're also given the cost per unit so again the unit is the same as kilowatt R so the cost per unit is 4 rupees per unit unit is kilowatt are all right so what do we do well again we have to figure out how many kilowatt ours is the energy consumed and once we know that we know for each kilowatt are four rupees and so then we can go ahead and do the algebra the only problem is we see that the power is not given in kilowatts power is given in watts so how do we do that that's the first thing we need to do we need to convert it so let's see one kilowatt I know is a thousand watt but what is 1 watt equal to well I'll divide by thousand on both sides and then we will see that one watt so this cancels one word is equal to 1 or thousand kilowatts one over thousand kilowatt so we can go ahead and write that this will be twenty times one watt is one over thousand kilowatt so this will be one over a thousand kilowatt so this cancels so it'll be two hundred to over hundred kilowatt and what's the time time is five hours per day but we are using it for 30 days so what is it total time well we'll multiply them that's going to be 30 times five that's used for 150 hours in total all right 30 times 5 is 150 so now we have what we want we have the power in kilowatt and we also have the time in ours we can go ahead now and calculate how many kilowatt R is being used so if you've not done this before pause the video and now try it all right let's do this so the energy I don't know where to write this let's put a bar here okay let's do that so the energy consumed would be kilowatt our that'll be two over hundred to over 100 times 150 150 kilowatt our I am directly writing the unit's here kilowatt R and that's going to be let's see two times 150 is 300 so 300 divided by 100 that's going to be three kilowatt R or three units and we know for each unit we have to pay four rupees so for three units how much should we pay oh for three units we are gonna pay four times three that is just 12 rupees so the cost is going to be three times four rupees that's going to be 2-valve rupees and we have solved our problem so whenever we are asked to calculate or ask to find the cost of operation and we are given the cost per unit remember that the word unit always means kilowatt ours so this gives us a clue that we need to first find the energy consumed in kilowatt ours to do that we have to make sure our power is always in kilowatts and the time is always in ours you multiply them will get the energy in kilowatt hours once we do that we are pretty much done then all we have to do is find the cost for so many kilowatt hours