(a) Find the individual monthly (30-day) electric energy costs (to the nearest dollar) for each

step 1 Let's start from the first part of this problem. In this problem, we have to calculate the month

(a) Find the individual monthly (30-day) electric energy...

Key Concepts

Electric Energy Consumption

This concept involves understanding that energy consumption is determined by the power rating of an appliance (typically in watts) multiplied by the amount of time it is in use. It connects the relationship between power, time, and energy delivered (usually measured in kilowatt-hours), which is a core idea in determining both energy use and associated costs.

Unit Conversion

Accurate calculations require consistent units for power and time. Converting minutes to hours or days to seconds ensures that calculations are correctly made. This concept is essential in many practical scenarios where different units of measurement are used for various quantities.

Utility Rate and Energy Cost Calculations

This key concept involves the process of translating energy consumption into monetary cost by using a given utility rate (cost per kilowatt-hour). It requires multiplying the total energy used by the rate, which allows the estimation of the financial outlay associated with energy usage.

Duty Cycle

Duty cycle refers to the fraction of time an appliance is actually operating compared to a total time period. Understanding this concept is crucial for determining effective or average power consumption when appliances do not run continuously, which influences energy usage and cost calculations.

Percentage Contribution Calculation

This involves determining what percentage each component (or appliance) contributes to a total measurement, such as the overall monthly cost. It requires calculating the ratio of each individual cost to the total cost and then expressing that ratio as a percentage, which is important for analyzing the impact of individual items.

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits stating that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance (V = IR). This concept is essential for understanding how voltage, current, and resistance interact in operating appliances.

Electrical Resistance and Current Calculation

This concept involves applying formulas from basic circuit theory to determine either the resistance or current of an appliance when operating. By knowing the operating voltage and the power rating, one can compute the current draw and, subsequently, the effective resistance of the appliance, which is important in circuit analysis and design.

Transcript

00:03 Let's start from the first part of this problem.

00:07 In this problem, we have to calculate the monthly electric energy cost for each appliance.

00:13 We can write the equation for the monthly cost of appliance as the cost will be equals to energy consumed by the appliance in kilowatt hours in a day or in a month.

00:29 So this is the energy in kilowatt hour in a month.

00:37 Otherwise, we have to multiply by 30 to get the energy consumed by this appliance in a month, multiply by the price per unit or rate per unit.

00:52 So we have to use this formula to calculate the cost for each appliance.

00:58 So let's start from the first one.

01:02 In the first case, we have an air conditioner.

01:10 So we have air conditioner.

01:13 Let's write the energy for this air conditioner.

01:16 So we can write is equal to power multiple.

01:18 By time so for the air conditioner we can get the values from the table and it is 500 to 5 ,000 so forth into 30 % of the total time that is a 30 divided by 100 multiply by 30 and then we have to convert these days into hours and we have to multiply by 40 yards so from here we will get the energy for this energy consumed by this air conditioner in a month which is equals to 180 kilowatt hour now we can write the cost for this appliance so monthly cost will be cost is equals to into 180 kilowattr into the rate per unit or per kilowatt that is equals to 0 .12 per kilowatt hour that is equals to 0 .12 per kilowatt so this will give us the value for this cost as $130.

02:34 So this is the answer, in the case of air conditioner.

02:40 In the second case, we have blender.

02:47 So for blender, we can write the total energy consumed in a month as is equal to into power which is equals to 800 watt into the consumption time that is equals to 0 .5 0 r per month into one month.

03:11 So from here we will get the value for this e as is equals to 6 .4 kilowattr.

03:24 Now the cost is written as cost is equals to into 6 .4 kilowattr into 0 .12 per kilowattr.

03:37 So from here we will get the value for this this cost as zero dollars so this is the approximate value not the exact value in the case three we have dishwasher so here we have dishwasher so for the dishwasher we can write the energy he as is equals to into 1 ,200 watt into 8 .0 hours per month into one month so from here we will get the value for the this e as 0 .76 for this e as 9 .6 kilowatt per hour so the energy consumption will be equals to 9 .6 kilowatt hour the corresponding cost will be cost is equal to into 9 .6 kilowattr into 0 .12 dollars per kilowattar so we will get approximately equals to one dollar.

05:13 So this is the cost of the dishwasher.

05:19 Move to the case four.

05:22 Here we have microwave.

05:30 So the energy will be e and this is written as e is equals to 900 watt into 15 divide by 60 hours into 30 days.

05:47 So the total energy will be equals to 6 .75 kilowattar.

05:56 And the corresponding cost will be cost is equal to into 6 .75 kilowattar into 0 .12 dollars per kilowattar.

06:13 So we will get the value for this cost as $1.

06:20 So we will get approximately equals to $1.

06:28 Similarly, we can white the energy for refrigerator.

06:35 The case of refrigerator, we have e as e is equal to into 500 watt into 15 divided by 100, multiplied by 30 into 24 hours.

07:00 So we will get the energy as 54 kilowattar the corresponding cost is written as cost is equals to into 54 kilowattar into 0 .12 per kilowattar so this will give us the cost as approximately equals to six dollar that's great now let's calculate the energy consumed by the stove.

07:47 This contains both burner and oven.

07:53 So in this case, the energy will be written as e.

07:57 And this is equal to into 6 ,000 plus 4 ,500 into 10 hours per month into one month.

08:17 So we will get the energy for the stove as e is equals to 100 into 5 ,000.

08:25 Kilowatt hour.

08:29 Now the corresponding cost will be cost is equal to into 105 kilowatt r into 0 .1 two dollars per kilowatt hour so this will give us value for the cost as one dollar.

09:02 The next is the tv for tv we can write the energy as e and this is equals to 100 watt and the time consumption time is 120 hours per month into one month so we will get the value for this e as 12 kilowatt r so it will be 12 kilowatt hour so this is the energy consumed by this tv so the corresponding cost will be cost is equal to into 12 kilowatt hour into 0 .12 per kilowattr so the cost will be equals to one dollar.

10:08 So we have done the first part of this problem...

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