8.1.4 Solenoid

A solenoid is a long coil made up of a numbers of turns of wire.

Magnetic Field Pattern

  1. Figure (a) illustrates the field pattern produced by a solenoid when current pass through it.
  2. The field lines in the solenoid are close to each other, indicates that the magnetic field is stronger inside the solenoid.
  3. We can also see that the field lines are parallel inside the solenoid. This shows that the strength of the magnetic filed is about uniform inside the solenoid.
  4. We can also see that the magnetic field of a solenoid resembles that of the long bar magnet, and it behaves as if it has a North Pole at one end and a South Pole at the other.

(Figure (a): Magnetic field pattern of a solenoid)

Determining the Pole of the Magnetic Field

  1. The pole of the magnetic field of a solenoid can be determined by the Right Hand Grip Rule.
  2. Imagine your right-hand gripping the coil of the solenoid such that your fingers point the same way as the current. Your thumb then points in the direction of the field.
  3. Since the magnetic field lines always come out from the North Pole, hence the thumb points towards the North Pole.

[Figure (b)]
  1. There is another method can be used to determine the poles of the magnetic field forms by a solenoid.
  2. Try to visualise that you are viewing the solenoid from the 2 ends as illustrated in figure (c) below.
  3. The end will be a North pole if the current is flowing in the aNticlockwise, or a South pole if the current is flowing in the clockwiSe direction.

Strength of the Magnetic Field

The strength of the magnetic field can be increased by
  1. increasing the current,
  2. increasing the number of turns per unit length of the solenoid,
  3. using a soft-iron core within the solenoid.

 

8.1.3 Current in a Coil

Field Pattern

  1. Figure (a) below shows the field pattern produced by a current flowing in a circular coil.
  2. In SPM, you need to know the field pattern, the direction of the field and the factors affect the strength of the field.
  3. The direction of the field can be determined by the Right Hand Grip Rule. Grip the wire at one side of the coil with your right hand, with thumb pointing along the direction of the current. Your other fingers will be pointing in the direction of the field.
Figure (a)
  1. Figure (b) shows the plan view of the field pattern.

Factors Affecting the Strength

There are 3 ways to increase the strength of the magnetic field:
  1. increase the current and
  2. increase the number of turns of the coil.
  3. use coil with smaller radius

 

8.1.2 Current in a Straight Wire

Magnetic Field Pattern

(Figure (a))
  1. The magnetic field generated by a straight wire are concentric circles around the wire as shown in figure (a) above.
  2. Take notes that when the direction of the current is reversed, the direction of the magnetic field line is also reversed.
  3. The direction of the magnetic field line can be determined by the Maxwell's Screw Rule or the Right Hand Grip Rule.

(Figure (b): The plan view of the magnetic field generated by a straight wire)
  1. Sometime, the magnetic field pattern may be given in plan view, as shown in figure (b).
  2. In plan view, a dot in the wire shows the current coming out from the plane whereas a cross in the wire shows the current moving into the plane.
(Figure (c): A dot indicates the current move out from a plane whereas a cross indicates the current move into the plane)

Direction of the Magnetic Field

The direction of the magnetic field formed by a current carrying straight wire can be determined by the
  1. Right Hand Grip Rule or the 
  2. Maxwell Screw Rule.

Right Hand Grip Rule

Grip the wire with the right hand, with the thumb pointing along the direction of the current. The other fingers give the direction of the magnetic field around the wire. This is illustrated in the figure below.
(Figure (d))

The Maxwell's Screw Rules
The Maxwell Screw Rules sometime is also called the Maxwell's Corkscrew Rule. Imagine a right handed screw being turn so that it bores its way in the direction of the current in the wire. The direction of rotation gives the direction of the magnetic field.

(Figure (e))


Strength of the Magnetic Field

  1. The strength of the magnetic field form by a current carrying conductor depends on the magnitude of the current.
  2. A stronger current will produce a stronger magnetic field around the wire as shown in Figure (f) below.
    (Figure (f))
  3. The strength of the field decreases out as you move further out. This is illustrated in figure (g) below. Thus, you must be very careful when you are asked to draw the magnetic field in your exam.
    (Figure (g)
  4. The distance of the field lines must increase as it is further out form the wire.

 

8.1.1 Electromagnetism

Magnetism

In form 3, we learned that
  1. a magnet can attract certain type of metal.
  2. the metals that can be attracted by a magnet are called the “magnetic materials” of “ferromagnetic materials”. Examples of magnetic materials are iron, steel, nickel and cobalt.
  3. a magnet has 2 poles-the North Pole and the South Pole.
  4. there is a magnetic field surrounding the magnet.  A magnetic field is a region in the surrounding of a magnet which a magnetic material experiences a detectable force.


Magnetic Field Line

(The magnetic field is represented by the magnetic field lines)
  1. The magnetic filed of a magnet is represented by the magnetic field lines. The magnetic field lines flow  out from the North pole and flow into the South pole.
  2. The distance between the field lines represent the strength of the field, the closer the field line, the stronger the field. In the diagram, the magnetic field A is stronger than magnetic field B because the line in magnetic field A is closer.

Compass in a Magnetic Field

(Figure(a): The pointer of a compass point towards the North pole of a magnet)


(Figure(b): The direction of the pointer of a magnet is always in the same direction of the magnetic field)
  1. The pattern and the direction of a magnetic field can be determined by a compass.
  2. First of all, we need to know that, in SPM, normally we use a circle with an arrow to represent compass. The arrow represents the pointer of a compass and it always points towards the North pole of a magnet.
  3. Second, we also need to know that the pointer of a compass is always in the direction of the magnetic field.
  4. In figure (b) above, we can see that when a few compasses are put near to a bar magnet, the pointer of the compasses are all in the direction of the magnetic field.
  5. If a compass is placed near to a current carrying wire, the pointer of the compass will point along the direction of the magnetic field generated by the current (as shown in the figure below). This will be discussed in electromagnetism.

  1. When current passes through a conductor, magnetic field will be generated around the conductor and the conductor become a magnet. This phenomenon is called electromagnetism. 
  2. Since the magnet is produced by electric current, hence it is called the electromagnet.
  3. An electromagnet is a type of magnet in which the magnetic field is produced by a flow of electric current. The magnetic field disappears when the current ceases.
  4. The magnetism of an electromagnet is switched on or off using electric current.
  5. In short, when current flow through a conductor, magnetic field will be generated. When the current ceases, the magnetic field disappear.

An electromagnet is a type of magnet in which the magnetic field is produced by a flow of electric current.

 

7.5.4 Energy Efficiency

Efficiency of Electrical Appliance

  1. The efficiency of an electrical appliance is given by the following equation eq1
  2. Normally, the efficiency of an electrical appliance is less than 100% due to the energy lost as heat and the work done against friction in a machine.


Example 1
A lamp is marked “240V, 50W”. If it produces a light output of 40W, what is the efficiency of the lamp?

Answer:


Example 2
An electric motor raises a mass of 2kg to a height of 5m in 10s. If the input current from a source of 12V is 2A, find the efficiency of the electric motor.

Answer:
Input power,
P = IV
P = (2)(12) = 24W

Output power




Steps to Save Electricity

  1. Use efficient lighting
  2. Buy efficient electric appliances.
  3. Use appliances with automatic power off function.
  4. Choose electrical appliances of sizes and features which best suit your needs.
  5. Proper utilization of all electrical appliances
    1. Defrost refrigerators regularly
    2. Run your washing machine only when it is fully loaded & Iron your clothes only when you have at least a few pieces to iron.
    3. Regular cleaning of air filters in air-condition units and clothes dryers. 

 

7.5.3 Power Rating and Energy Consumption

Power Rating

  1. Figure above is an example of power rating label.
  2. An electrical appliance which is marked 240V, 1200W means that the electrical appliance will consume 1200J of energy in every second if the potential difference across it is 240V.


Example
A bulb rated 240V/80W is operated from a 120V power source. Find the resistance and the current flows through it.

Answer:


The current flows through the bulb


Energy Consumption

Calculating the cost of electricity consumption

  1. The amount of electrical energy consumed in a given time:
  2. The larger the power rating in the electrical appliance, the higher energy is used for every second. 
  3. The longer the usage time, the higher electrical energy is consumed.
  4. The cost of electricity consumption is based on the number of kilowatt-hours (kWh) of electrical energy used. 
  5. The kilowatt-hours are sometimes known as the domestic units of electricity.
  6. The kilowatt-hour (kWh) is the energy used by a device at a rate of 1000 watts in one hour.
    1 kWh = (1000 W) × (60 × 60 s) = 3.6 MJ


Example:
If TNB charges 22 cents for each kWh of electrical energy used, calculate the total cost of using a 2kW electric kettle for 15 minutes and a 20 W filament bulb for 8 hours.

Answer:
Electrical energy consumed by the kettle,


Electrical energy consumed by the bulb,


Total energy consumed,


Cost = 0.66 x 22 cent = 14.52 cent

 

7.5.2 Power

  1. The electric power, P is defined as the rates of energy that supply to the circuit ( or the rates of work been done ) by sources of electric.
  2. The unit of electric power is the watt (W).
  3. One watt of power equals the work done in one second by one volt of potential difference in moving one coulomb of charge.
  4. The electrical power of an electric circuit component can be find from the following equations:


  5. Where
    P = power/4
    t = time
    I = current
    V = potential difference
    R = resistance

Example 1:
A current of 0.50A flows through a 100Ω resistor. What is the power lost in the resistor?

Answer:


Example 2
An electric iron has a heating element of resistance 50Ω. If the operating current flowing through it is 4A, calculate the heat energy produced in 2 minutes.

Answer:
Power of the iron,

Heat energy produced,


Example 3
What is the power dissipated in a 4Ω light bulb connected to a 12V battery? What is the power dissipated in a 2Ω light bulb connected to the same battery? Which bulb is brighter?

Answer:
Assume that the bulbs are resistor


Power dissipated in the 4Ω resistor,

Power dissipated in the 2Ω resistor,

The power of the 2Ω bulb is higher, hence it is brighter.

[Conclusion: The lower the load resistance in a circuit, the greater the power dissipated in the circuit]


Example 4

An ideal battery with e.m.f. 12 V is connected in series to two bulbs with resistances R1 = 4Ω and R2 = 2Ω  What is the current in the circuit and the power dissipation in each bulb?

Answer:
Potential difference across the 2 resistors, V = 12V
Equivalence resistance of the 2 resistors, R = 4 + 2 = 6Ω
Current in the circuit,


Power dissipated in R1


Power dissipated in R2


[Conclusion: In a series connection, the greater the resistance of a resistor, the greater the power dissipated]


Example 5


The figure above shows that an ideal battery is connected in parallel to two resistors with resistances 2Ω and 4Ω. Find the power dissipated in
a. the 4Ω resistor
b. the  2Ω resistor

Answer:
a. The potential difference across the 2 resistor = 12V
The power of the 2Ω resistor,


b.
The power of the 4Ω resistor,


[Conclusion: In a parallel connection, the lower the resistance, the greater the power of the resistor.]

In a circuit of any connection (series or parallel), the power dissipated in the whole circuit is equal to the sum of the power dissipated in each of the individual resistor.

Example 1:
2 identical bulb of resistance 3Ω is connected to an e.m.f. of 12V. Find the power dissipated in the circuit if
a. the bulb is connected in series
b. if the bulb is connected in parallel

Answer:
a.

Current pass through the 2 resistors,


Power of each of the resistor,


Sum of the power,



b.


Potential difference across the 2 resistor = 12V
Power of each of the resistor,

Sum of the power,


Example 2:
A 800W heater is used to heat 250 cm³ of water from 30 to 100°C. What is the minimum time in which this can be done? [Density of water = 1000kg/m³; Specific Heat Capacity of water = 4200J°C-1 kg-1]

Answer:
Energy supply by the heater, E = Pt

Heat energy absorbed by the water, E = mcθ

Let's assume that all the energy supplied by the heater is converted to heat energy and absorbed by the water, hence

 

7.5.1 Electrical Energy

  1. From the definition of potential difference, the electrical work done is given by the equation W = QV, where
    W = work
    Q = charge
    V = potential difference
  1. Since the work done must be equal to the energy to do the work, therefore we can also say that, the electrical energy ( E ) is also given by the formula

Example
Given that the potential difference across a bulb is 240V and the current that flow through the bulb is 0.25A. Find the energy dissipated in the bulb in 30s.

Answer:
Formula of current,
E = QV
hence
Q = It

Energy dissipated,

E = QV
E = (It)Q
E = (0.25)(30)(240)
E = 1800V

 

7.4.2 Internal Resistance

The internal resistance of a source (cell or generator) is the resistance against the moving charge in the source.

Load Resistance

The load resistance in a circuit is the effective resistance against the moving charge outside the source of electric.

Terminal Potential Difference

Terminal potential difference or terminal voltage is the potential difference across the two terminal (the positive terminal and the negative terminal) of an electric source (cell or generator).

Internal Resistance and Potential Difference Drop

  1. If the internal resistance is ignored, the terminal potential difference is equal to the e.m.f.
  2. If the internal resistance is present, the terminal potential difference will be lower than the e.m.f.
  3. The relationship between e.m.f. and the terminal potential difference is given by the following equation.
    Equation
    E = V + Ir
    or
    E = IR + Ir

    E = e.m.f.
    V = terminal potential difference
    I = current flows in the circuit
    r = internal resistance
    R = the load resistance

Example 1:
A cell has internal resistance 0.5Ω and the potential difference across the cell is 4V when a 2A current flows through it. Find the e.m.f. of the cell.

Answer:
r = 0.5Ω
V = 4V
I = 2A
E = ?

E = V + Ir
E = (4) + (2)(0.5)
E = 5V

Example 2:

A cell with e.m.f. 3V and internal resistance, 1Ω is connected to a 5Ω resistor, and a voltmeter is connected across the resistor as shown in the diagram on the left. Find the reading of the voltmeter.

Answer:
E = 3V
r = 1Ω
R = 5Ω
V = ?

E = I(R + r)
(3) = I(5 + 1)
3 = 6I
I = 3/6 = 0.5A

V = IR
V = (0.5)(5)
V = 2.5V

Measuring e.m.f. and Internal Resistance



Three methods can be used to measure the e.m.f. and internal resistance.
  1. Open circuit-Close circuit
  2. Simultaneous equation
  3. Linear Graph
Open Circuit
In open circuit ( when the switch is off), the voltmeter shows the reading of the e.m.f.

Close Circuit
In close circuit ( when the switch is on), the voltmeter shows the reading of the potential difference across the cell.

With the presence of internal resistance, the potential difference across the cell is always less than the e.m.f..

Example 1:


The diagram above shows a simple circuit that connect some baterries to a resistor. The voltmeter shows a reading of 5.0V when the switch is off and 4.5V when the switch is on. What are the e.m.f. and the internal resistance of the cell?

Answer:
When the switch is off, the reading of the voltmeter shows the e.m.f. of the batteries. Therefore.
e.m.f. = 5.0V

When the switch in turned on, the reading of the voltmeter shows the potential difference of the resistor. Therefore,
V = 4.5V

The current that pass through the resistor,

E = V + Ir
(5.0) = (4.5) + I(0.5)
0.5I = 5.0 - 4.5
I = 0.5/0.5
I = 1A


Example 2:
Diagram (a)
Diagram (b)


A cell is connected to a circuit as shown in diagram (a). The graph in diagram (b) shows the change of the reading of the voltmeter, V against time, t. If t is the time where the switch is close, find
(a) the e.m.f. of the cell
(b) the internal resistance of the cell.

Answer:
(a) Before the switch turned on, the reading of the ammeter shows the e.m.f. of the cells.

From the graph, the e.m.f. = 3.0V

(b)
e.m.f., E = 3.0V
Potential difference across the resistor, V = 2.5V

Current that pass through the resistor,


 

7.4.1 Electromotive Force

  1. In a circuit, electromotive force is the energy per unit charge converted from the other forms of energy into electrical energy to move the charge across the whole circuit.
    In equation,

  2. where
    E = e.m.f.,
    W = energy converted from non-electrical forms to electrical form
    Q = positive charge.
  1. The unit of e.m.f. is JC-1 or V (Volt)
  2. The unit of e.m.f. is JC-1 or V (Volt). Electromotive force of 1 Volt means that 1 Joule of electrical energy is supplied to the circuit to move 1 Coulomd of charge across the whole circuit.

Electromotive Force
Potential Difference
Similarities:
Have same unit (Volt)
Can be measured by Voltmeter
Definition
The electromotive force (e.m.f.) is defined as the energy per unit charge that is converted from chemical, mechanical, or other forms of energy into electrical energy in a battery or dynamo.
Definition
The potential difference (p.d.) between two points is defined as the energy converted from electrical to other forms when one coulomb of positive charge passes between the two points.
Symbol:
Denote by the symbol, E.
Symbol:
Denote by the symbol, V

Example 1
When a 1Ω resistor is connected to the terminal of a cell, the current that flow through it is 8A. When the resistor is replaced by another resistor with resistance 4Ω, the current becomes 2⅔A. Find the
a. internal resistance of the cell
b. e.m.f. of the cell

Answer:
Experiment 1
R1 = 1Ω
I1 = 8A


Experiment 2
R2 = 4Ω
I2 = 2⅔A


Solve the simultaneous equation
E = 12V, r = 0.5Ω


Example 2
The diagram on the left shows that the terminal potential difference of a batteries is 1.2V when a 4 Ω resistor is connected to it. The terminal potential become 1.45V when the resistor is replaced by another resistor of resistance 29Ω
Find the
a. internal resistance, r
b. e.m.f. of the batteries.
Answer:
Experiment 1

V1 = 1.2V
R1 = 4Ω

I = V/R
I = (1.2)/(4)
I = 0.3A


E = V + Ir
E = (1.2) + (0.3)r
E - 0.3r = 1.2 ------------(eq1)

Experiment 2
V2 = 1.45V
R2 = 29

I = V/R
I = (1.45)/(29)
I = 0.05A

E = V + Ir
E = (1.5) + (0.05)r
E - 0.05r = 1.45 -----------------(eq2)

Solve the simultaneous equation eq1 and eq2

E = 1.5V, r = 1Ω

The Linear Graph


From the equation,

E = V + Ir
Therefore
V = -rI + E

Y axis = Potential difference (V)
X axis = Current (I)
Gradient od the grapf, m = - internal resistance (r)
Y intercept of the graph, c = e.m.f.

Example:

The graph shows the variation of potential difference with current of a battery.
What is the internal resistance and e.m.f. of the battery?

Answer:
e.m.f. = y-intercept = 3V

internal resistance,
r = -gradient of the graph
r = - (-3)/(6) = 0.5Ω