Electric Energy and Electrical Power

The electric energy (E) can be defined as the work done to move a certain charge Q-across a potential difference V and is measured in Joules, thus

                         E = Q^.V

E = V.I.t = I². R.t = ^.t

The electric energy changes from one form to another, e.g. electric energy is converted to heat energy in the conductor which raises its temperature, or can be converted to motion or light or sound.

The electric power is the rate of change of energy and measured in J/s or watts (W) i.e.

P =  =  = V^.I = I^2. R^. = .W

The power output of a battery = ^{…………………..}

The power dissipated in a resistor= ^{……………………..}

Example:

A. p.d. of 12 V is applied across 4 W resistor.  Find the power dissipated in the resistor.  Calculate the thermal energy produced in 15 s.?

Solution

P =  =144/4 = 36 W

     Electrical energy dissipated in the resistor = Thermal energy produced

                     = P^. t = 36^. 15 = 540 W.s. = 540 J

Commercial Unit of electric energy

In industry , a large unit of energy is used, it is called the "kilowatt hour" (KWh)

1 KWh = (1000 W) x (3600 s) = 3 600 000 W .s

= 3 600 000 Joules = 3.6 MJ

Electrical Energy Calculation and Costs

Example:

    A small water heater is connected to a 12 V supply.  If the heater element has a resistance of 3 W, how much thermal energy is given off in 5 minutes?

Solution

E = t =(144/3) 300 = 14400 J

Thermal energy given off by the heater = Electrical supplied by the heater = 14400 J

Example:

     If an electrical energy costs 5 p per unit, what is the total cost of leaving 4 light bulbs rated at 100 W each, switched on for 8 hours and a water heater of power 1.2 KW is switched on for 30 min.

Solution

      Electrical energy consumed by the four lamps

= 4^.100^.8/1000 = 3.2 KWh

     Electrical energy consumed by the heater = 1.2^. (30/60) =0.6 KWh

House Electrical Installations

A simple AC mains circuit

When you plug into the mains(sources), electrical energy comes from a power station rather than a battery, but the same circuit basic principle apply.

Unlike the one way current (d. c.) from a battery, the current from the mains socket is pushed and pulled forwards and backwards from the circuit 50 times every second.  This current is known as alternating current (a. c.).  Power stations supply a. c. because it is easier to generate than d. c.  the symbol for a. c. is as shown in the following figures.

       Or     

Circuit parts and elements

1. Live wire:  The potential of this wire goes alternately negative and positive making the current flows backwards and forwards.

2. Neutral wire:  This wire is connected to earth.  Although the current passes through this wire, it remains at zero potential.  If you accidentally touch it, you don't get a shock.

3. Switch: The switch is fitted in the live wire.  The switch would work equally well in the neutral, but wire in the flex would then still be live when the switch was turned off.  This would present a hazard if, for example, the cable were broken accidentally.

4. Fuse: This is a short piece of thin wire which overheats and melts if a current of more than a certain value flows through it.  Like the switch it is place in the live wire, often in the form of a small cartridge inside the plug.  If a fault developed in a device, a too high current flows, the fuse blows and breaks the circuit before the cable can overheat and catch fire.  The fuse value should be little bit larger than the rated full load current of the circuit.

5. The earth wire: This is a safety wire which connects the metal body of the device to the earth and prevents it becoming live if a fault develops.  If for example the live wire were to work loose and touch the body of the device, a current would immediately flow to earth and blow the fuse.

6. Circuit breaker: Circuit breakers are now used instead of fuses.  They have an electromagnet.  If the current is exceeds certain value (rated value of the circuit breaker), the electromagnet becomes strong enough to separate a pair of contacts and breaks the circuit.

Colour code:

The live wire is brown,

the neutral wire is blue, and

the earth wire is green-yellow

The following figure shows a simple schematic diagram for house circuit.

You may note the following:

1. All lamps and appliances are connected in parallel.  Why?

2. All switches and fuses must be placed in the live side.

3. The earth wire is connected between the metal casing of appliances and the earth.  (plastic casing does not need earthing

Dangers of Electricity :

The main hazards of electricity are due to :

(i) Damaged insulation of wires.

(ii) Overheating of cables due to large currents.

(iii) Damp conditions which break down the insulation.

Why are all appliances and lamps in a house connected in parallel.

This is done for several reasons :

I. The voltage across each component equals the voltage of the mains (large V).

II. The total resistance of several component in parallel is very small; thus the

current from the mains becomes large, (large current in each component).

III.The power ( or brightness) of each component becomes high ( since p = I V)

IV. . Each component or lamp can work independently by a separate switch in its branch.

Note: If appliances and lamps are connected in series, opposite results occur with obvious disadvantages.

Potential Divider (Voltage divider)

A battery provides a n e.m.f.  For example a 12 V battery provides 12 V only. However, we often wish to use only a part of this voltage, so we use a potential divider circuit as shown in the following figures.

The following figures show the use of potential divider to control the voltage applied to lamp in order to control the brightness of a lamp.

Connect a battery to the variable resistor so that the fixed voltage of the battery , V; , is applied across the full length of the resistance, R, , and the lamp is connected to the slider S.  As the slider is moved to different positions, the voltage across BS (lamp voltage) is proportional to the resistance R₁ between B and S, thus

The voltage across lamp increase as R₁ increases (as S moves towards A) and decreases as R₁ decreases (as S moves towards B)

The rheostat acts as a voltage divider or a potentiometer which enables you to choose the proper voltage.  It is used as a volume control in radios and other circuits.

Note: "The potential difference across the lamp (or apparatus) is directly proportional to the resistance across it".

Example: Find the voltage across the lamp in the following figures

Example: Find the voltage across the 200 W in the following figure

Magnetic Effects of a Current

Experiments showed that an electric current in a wire produces a magnetic field around it, which causes the deflection of the magnetic needle of a compass.

1) Magnetic flux pattern due to a current in a straight wire :

The iron filings on the cardboard shows that the field lines are concentric circles around the wire. A compass can be used to show the direction of field lines.

Right-hand grip rule :

Grasp the wire in right hand and with thumb pointing along the wire in the direction of the current.

The direction of the fingers gives the direction of the magnetic flux.

The magnetic field produced increases as the current is increased, and it becomes weaker as you go away from the wire.  If the current is reversed, the direction of magnetic flux is also reversed.

2) Magnetic flux due to a current in a Circular Coil :

The magnetic flux is circular around each section of the coil.  At the center, the magnetic field is almost straight and is perpendicular to the plane of the coil.

3) Magnetic flux due to a current in a Solenoid :

The magnetic field produced is similar to that of a permanent magnet having  two poles, north and south. Inside the solenoid, the magnetic field is uniform.

The polarity produced in the solenoid is found by the right-hand grip rule:  When the fingers of the right hand turn in the direction of the current, the thumb will point towards the North pole

The magnetic field of the Solenoid can be increased by

(i) increasing the current

(ii) increasing the number of turns(i.e, length of the wire )

(iii) inserting a soft iron bar in the solenoid.

Electromagnet:

An electromagnet is made of a solenoid wound around a core made of soft iron.  It is magnetized only during the flow of current, when the current is switched off it loses its magnetization, its magnetism is only temporary.

Electromagnets are used in: electric bells, magnetic relays, telephone receivers,

The electric bell

An electric bell contains an electromagnet that switches itself off and on very rapidly, moving the bell hammer as it does so. The action is shown in the figure.

The magnetic relay

A magnetic relay is a switch operated by an electromagnet. The magnetic relay shown in the figure is being used to control the circuit connecting a battery to an electric motor .

ELECTRIC MOTORS

A current-carrying conductor in a magnetic field

Hang a flexible wire perpendicular to field between the poles of a strong magnet. Connect the wire to a source of direct current through a switch. The moment you press the switch the wire will move away from the magnet. Now, reverse the direction of the current keeping other things unchanged, the wire will move towards the magnet when the switch is pressed. Instead of reversing the direction of the current, turn over the magnet to reverse the magnetic field, you will find that the wire will change its direction of motion, to move towards the magnet. So, the conclusion is that:

(1) A wire carrying current placed perpendicular to a magnetic field experiences a force perpendicular to the direction of both the current and the magnetic field.

Magnetic field + perpendicular electric current

Force (motion)

(2) This force reverses its direction on reversing the direction of the electric current or the magnetic field.

Fleming's left hand rule

This rule is used to determine the direction of movement (Force) when the directions of current and field are known.  As shown, place forefinger, second finger and thumb of left hand mutually at right angles. Then,

"If Forefinger points in the direction of the Field, and
seCond finger points in the direction of the Current,
the thuMb will point in the direction of the Motion"

Note : If the wire is parallel to the field no force is produced.

A Beam of charged particles in a magnetic field

Consider a beam of positively charged ions accelerated to velocity v.  If this beam of charges enters a magnetic field at right angle to its direction of motion, the beam will experience a force perpendicular to both velocity and magnetic field.

The beam of charges will deflect in a circular path.

If the particles of the beam move parallel to the magnetic field, no force is produced.  To know the direction of the force, one can apply Fleming's left-hand rule.

If the charges are negative, say a beam of electrons, the direction of the current is taken to be opposite to the direction of electron motion

Current-carrying coil in a magnetic field

Consider a loop of a conducting wire which can rotate about an axis. Place this loop in the field between the poles of a strong magnet.

Connect the loop, through flexible wires, to a battery as shown in figure.  When the electric current passes through the loop, an upward force will act on the side near the north pole according to Fleming's left-hand rule. The other side also will be acted upon by a downward force.  These two forces will form a couple which turns the loop in a clockwise direction.

When the face of the coil is at right angles to the field, the forces have no turning effect because both act in the same line.  The couple becomes zero and the coil comes to rest in a vertical position.

The Simple motor

If we want to keep the loop turning in one direction we have to reverse the direction of the current in the loop each half a turn.  This is achieved by the use of a commutator, which looks like a copper ring cut into two halves. In this case current is passed in and out of the loop by brushes that press onto the commutator strips.

The brushes, usually made of carbon, do not go round so the wires do not get twisted.  This arrangement makes sure that the

(i) the current is reversed in the wires each half cycle,

(ii) the force on each wire is reversed each half cycle, but,

(iii) the rotation of the loop continues in the same direction.

At some instant when the loop is vertical the current stops flowing because the gaps in the commutator break the circuit.  However, the loop keeps turning because of its own momentum

The turning force could be increased by:

a) Using a coil of hundreds of turns instead of a loop or a single turn.

b) Increasing the current in the coil.

c) Increasing the magnetic field by using a strong magnet.

d) Using a soft iron core for the coil to concentrate the lines of the magnetic field.

Practical motors use

(1) rectangular coils made of very large number of turns,

(2) several coils set at small angle to each other, and several magnet poles, to get smoother running and constant turning force in all positions.

Electromagnetic Induction

(1) Move the wire downwards perpendicular to a strong magnetic field. The galvanometer pointer will deflect showing the flow of electric current.

(2) Now, reverse the movement of the wire, i.e. move it upwards, the galvanometer pointer deflects in the opposite direction.

(3) If you hold the wire still in the magnetic field the galvanometer reads zero, i.e., no current is flowing.

The induced current produced increases by:

(i) Using a stronger magnet.

(ii) Using a longer wire

(iii) Increasing the speed of motion.

Dr. Adel A. El-samahy