An incandescent lightbulb draws 261 mA, while an LED with the same light output draws 34.8 mA.

An incandescent lightbulb draws 261 mA, while an LED with...

An incandescent lightbulb draws $261 \mathrm{~mA}$, while an LED with the same light output draws $34.8 \mathrm{~mA}$. Both operate on standard $230-\mathrm{V}$ household power. (a) Determine their energy-consumption rates. (b) Suppose you've been operating the incandescent bulb for 3 hours a day and that your electrical energy costs $13.5$ pence per kWh. How much money will you save on your electric bills over a year if you replace the incandescent with the LED? Note than an incandescent lightbulb costs about $£ 0.7$, while you might pay $£ 7$ for an LED-and the LED will last many years.

Key Concepts

Electric Power Calculation

This concept involves determining the rate at which energy is consumed by using the formula P = V × I, where P is the power in watts, V is the voltage, and I is the current in amperes. It is fundamental in evaluating how much energy a device uses over time.

Energy Consumption and Unit Conversion

Energy consumption is the total amount of energy used measured typically in kilowatt-hours (kWh). It is calculated by multiplying the power rating (in kilowatts) of a device by its operating time (in hours). Understanding how to convert between watts and kilowatts and correctly compute kWh is crucial for comparing energy usage.

Electricity Cost Calculation

This involves calculating the cost associated with energy consumption by multiplying the energy used (in kWh) by the price per kWh. This method allows one to determine the financial impact of using different electrical devices over a period of time, providing a clear perspective on cost savings and efficiency.

Transcript

00:01 Hi, here for this given problem we know 1 pound is equal to 100 pence.

00:12 So first of all, current drawn by incandescent light bulb that is given as let it be i1 and its magnitude is 261 millie ampere.

00:40 And that by led, current drawn by led, that is given as i2 is equal to just 34 .8 millie ampere.

00:57 And household voltage, this is given as v, is equal to 230 volt.

01:11 In the first part of the problem, we have to find the rate of energy consumption for both.

01:17 So first of all, energy consumption rate of incandescent bulb, p1, energy consumption rate means its power, that is p1 is equal to v into i1, means 230 multiplied by 261 ampere, millie ampere or into 10th bar minus 3 ampere.

01:56 So this rate of energy consumption comes out to be equal to 60.

02:01 0 3 watt.

02:04 One of the answer for the first part of the problem.

02:09 Then in the same problem, in the first part of the problem, rate of energy consumption for led, that is p2 is equal to v into i2.

02:39 So this is 230 multiplied by 34 .8 millie -amper or into tenth bar minus 3 .3.

02:48 So this p2 is calculated to be equal to 8 .0 watt power for led.

02:59 Now in the second part of the problem, we have to compare the running cost for both of them in a year.

03:11 So total time for operating them in a year.

03:26 That will be 3 hours per day multiplied by 365 days.

03:33 So it comes out to be equal to...