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Electrical Energy and Power

 What is Work?

In classical physics terms, you do work on an object when you exert a force on the object causing it to move some distance. The amount of work you actually do may have little relationship to the amount of effort you apply.

For example, if you push on a car stuck in a snow drift, you may exert a lot of force (and effort) but if the car does not budge, you have not done any work! In order for work to be done on an object, the object must move some distance as a result of the force you apply. There are also constraints on the force you apply. Only force exerted in the same direction as the movement of the object result in work. You may think that you do a lot of work if you carry an arm full of books from home to school. In reality you do no work at all! In carrying the stack of books, you exert an upward force to hold the books so they don't fall to the ground. There is no movement associated with this force. As you walk, the motion of the books is horizontal not vertical. Since the force applied to the books is vertical, and the motion is horizontal, you do not do any work on the books.

Work is a transfer of energy so work is done on an object when you transfer energy to that object.      The amount of work done on an object depends on the amount of force exerted on the object and the amount of distance the object moves.                                                                                                                       The unit of the work is Newton-meters which are termed to joules (J).

 

Work = Force x Distance

                                                   OR      work done = energy transferred

   

  What is Energy?

Although wind is just moving air, it possesses energy. When the wind moves the leaf on a tree or picks up and hurls a truck, it has caused a change in the position of the object. Therefore it has done work.                  A measure of the ability to do work or cause change is called energy. Any time an object does work on another object, some of the energy of the working object is transferred to that object raising          its energy state. Like work, the units of energy are joules.

 There are two categories of energy, kinetic energy and potential energy. The difference between them is whether the energy is being transferred (kinetic) or stored (potential). They are inter-convertible.


  What is Power?

Energy is a measure of how much work can be done without any consideration of how long it takes to accomplish the work. Power is the measure of how quickly the work is done so it is a time-dependent function. Thus, two marathon runners do the same amount of work when they run the 42 kilometers. However, the runner that finishes the marathon in 2 hours runs twice as powerfully as the runner that finishes in 4 hours. Power is the amount of energy used per unit of time.

Power = Work/Time = (Force x Distance)/time

 

Units of Power

The unit of power is joules per second or J/s when work is measured in joules and time in seconds. The basic unit of power is (J/s) which is called a watt (W). By definition, a watt is the consumption of one joule of energy per second. 1 KW = 1000 W = 1000J/s

1 W = 1 J/s


                                          

                                    The Electrical Energy & the Electrical power 

electrical power


Electricity and energy:

We use electricity because it is a good way of transferring energy from place to place. In most places if you switch on an electric heater, you are getting the benefit of the electrical energy released as fuel is burned in a power station. 

Why do we use high voltages for our mains supply?

The reason is that a supply with high voltages gives a lot of energy to the electric charge that it pushes around the circuit. For example a 230 volt mains supply gives 230 joule of energy to each coulomb of charge that travels around the circuit.  

1 volt = 1 joule per coulomb.

The word "per" means "divided by",
so  voltage = energy ÷ charge.

This equation can be rearranged to give
energy = voltage x charge.  

 E = V x Q.

Since Q = I x t, if we write (I x t) instead of in the above equation we get

  E =x I x t.
Electrical Energy voltage x current x time.

We can also use the word work instead of the word energy

because as we mentioned before work done = energy transferred

so you might see the equation
energy = voltage x charge (E = V x Q) written as work = voltage x charge  (W = V x Q)


       as we mentioned power is the amount of energy that is transformed each second

                             So                                     Electrical power = Energy ÷ Time 

  P = E / t               but E =V.I.t

  P = V.I.t / t 

  P (watt) = V(volt) x I (amp)

        P =V x I

from Ohm's law    V= I x R     

P = I2 x R



Problems 


1- An electric iron operating at 120 volts draws 10 amp of current. how much heat   energy is delivered by the iron in 30 sec. 
 Sol.
 Write down what you know, and what you want to know.
V = 120 volts
I = 10 Amp
t = 30 sec.

E = V I t = 120 x 10 x 30                           E = 3600 J


2- A 110 volt toaster oven draws a current of 6 amps on its highest setting as it converts electrical energy to thermal energy. What is the toaster maximum power rating?
   Sol.
 Write down what you know, and what you want to know.
V = 110 volts
I = 6 Amp
P = I V     =  110 x 6                                  
 P = 660 watt

3- One watt is equivalent to one:
a- N.m
b- N/m
c- J.s
d- J/s                                                                    answer
                                                                               P= E/t
                                                                               watt = Joule/ sec ... answer will be(d)

4- A potential of 50 volts is measured across a 250 ohm resistor. What is the power developed in the resistor.
Sol.
 Write down what you know, and what you want to know.
V = 50 volts
R = 250 ohm                         I = ?                    P = ?
 V = I R                                  I = V/R                        I = 50/250 = 0.2 Amp
  P =  I. V                               P = 50 x 0.2
                                               P = 10 w      

5- What is the minimum information needed to determine the power dissipated in a resistor of  unknown value?
a- Potential difference across the resistor only.
b- Current through the resistor only.
c- Current and potential difference only.
d- Current, potential difference, and time of the operation.                  

answer is (d)

 


  Check your learning 


Activity no. 1     
Try to solve the attached work sheet below.










 Paying for electricity 

You can't watch TV all evening it will cost too much.

The amount of electrical energy transferred to an appliance depends on its power, and on the length of time it is switched    on for. 

The amount of mains electrical energy transferred is measured in kilowatt-hours (kWh). One unit is 1kWh.

The equation below shows the relationship between energy transferred, power and time:

energy transferred (kilowatt-hour, kWh) = power (kilowatt, kW) × time (hour, h)

Note that power is measured in kilowatts here, instead of the more usual watts. To convert from W to kW you must divide by 1,000.

For example, 2,000W = 2,000 ÷ 1,000 = 2kW.

Also note that time is measured in hours here, instead of the more usual seconds. To convert from seconds to hours you must divide by 3,600.

For example, 1,800s = 1,800 ÷ 3,600 = 0.5 hours.


The costElectricity meters

Electricity meters measure the number of units of electricity used in a home or other building. The more units used, the greater the cost. The cost of the electricity used is calculated using this equation:

cost = power (kW) × time (hour) × cost of 1 kWh (pence)


Question 1 :

An electric fire needs 2 kW. It is switched on for 3 hours. If each kWh costs 10p, how much does it cost to run the fire?

Answer

cost = power × time × cost of 1 kWh

       = 2 kW × 3 h × 10p

       = 60p


Question2: 

A TV needs 250 W. It is switched on for 30 minutes. If each kWh costs 8p, how much does it cost to run the TV?
toggle answer
Answer
cost = power × time × cost of 1 kWh
       = 0.250 kWh × 0.5 h
× 8p

       = 1p


Complete the following table:
Take the cost of 1 kWh to be 15p.
no.AppliancePowerTimeCostno.AppliancePowerTimeCost
1Kettle2.5 kW6 min 6Light bulb60 W4 hours 
2Iron.....(1).......2 hours30 p7Light bulb .....(4).......3 hours9 p
3Washing machine250 W45 min 8Hair drier0.15 kW .....(5).......5 p
4Stereo200 W ......(3)......15 p9Vacuum cleaner0.5 kW .....(6).......15 p
5Television .....(2).......4 hours22.5 p10Freezer120 W6 hours ......(7)......


Ċ
Faiza Ayoub,
7 Feb 2015, 23:43
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