Chapter 2 - Electricity (Form 5)

2.Electric Charge

1. There are only two kind of electric charge, namely the positive charge and the negative charge.

2. Like charge repel each other.3. Unlike charge attract each other.4. The SI unit of electric charge is Coulomb (C).

Unit of Charge

The SI unit of electric charge is Coulomb (C)

1Coulomb (C) = 1 Ampere Second (As)

Example

Charge of 1 electron = -1.6 × 10-19 C Charge of 1 proton = +1.6 × 10-19 C

Formula - Total Charge

Example 11.25×1019 electrons are added into an object. Find the nett charge of the object in the unit of Coulomb. [Charge of 1 electron = -1.6×10-19]

Answer:

Number of electrons, n = 1.25×1019Charge of 1 electron, e = -1.6×10-19Total charge, Q = ?

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Q = neQ = (1.25×1019)(-1.6×10-19) = -2C

Current

An electric current I is a measure of the rate of flow of electric charge (Q) through a given cross-section of a conductor.

Direction of Current

Conventionally, the direction of the electric current is taken to be the flow of positive charge.

The electron flow is in the opposite direction to that of the conventional current.

Unit of Current

The SI unit for current is the ampere (A).

Therefore, we can say that a current of one ampere is a flow of charge at the rate of one coulomb per second. (Note: This is not a definition of ampere.)

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Formula of Current

Example 2If 30 C of electric charge flows past a point in a wire in 2 minutes, what is the current in the wire?

Answer:

Charge, Q = 30CTime taken for the charge flow, t = 2 minutes = 120s(Since the unit of current, Ampere (A) is also equal to Coulomb per second (Cs-1), the unit of time must be changed to second)Current, I = ?

Electric Field

An electric field exists in a region of space where a small positive charge experiences an electric force.

Line of force

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1. The direction of the field is defined as the direction of the force on a small positive charge.

2. Lines of force are used to represent the direction of an electric field.3. The lines of force are directed outwards for a positive charge and inwards for a

negative charge.

Strength of Electric Field

The strength of the electric field is indicated by how close the field lines are to each other. The closer the field lines, the stronger the electric field in that region.

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Field Pattern of 2 Point Sources

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Ping Pong Ball in an Electric Filed

The ball will still remain stationary. This is because the force exert on the ball by the positive plate is equal to the force exerted on it by the negative plate.

If the ping pong ball is displaced to the right to touch the positive plate, it will then be charged with positive charge and will be pushed towards the negative plate.

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When the ping pong ball touches the negative plate, it will be charged with negative charge and will be pushed towards the positive plate. This process repeats again and again, causes the ping pong ball oscillates to and fro continuously between the two plates.

Candle in an Electric Field

The heat of the candle flame removes electrons from the air molecules around it, and therefore ionised the molecule.

If the candle is placed in between 2 plates connected to a Extra High Tension (E.H.T.) power supply, the positive ions will be attracted to the negative plate while the negative ions will be attracted to the positive plate.

Electrical Potential

The electric potential V at a point in an electric field is the work done to bring a unit ( 1 Coulomb) positive charge from infinity to the point.

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Potential Difference (Voltage)

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.

Unit of Potential Difference

The SI unit of potential difference is the same as that for e.m.f., i.e. the volt. We define the volt as follows:

The potential difference (p.d.) between two points in a conductor is 1 volt if 1 joule of energy is converted from electrical to other forms when 1 coulomb of positive charge flows through it.

Formula of Potential Difference

Example 1How much energy had been transfer when 5 C charges moved across a potential difference of 10V?

Answer:

The charge, Q = 5CPotential difference, V = 10VEnergy, E = ?

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Ohm's Law

The current flowing in the metallic conductor is directly proportional to the potential difference applied across it’s ends, provided that the physical conditions ( such as temperature ) are constant.

Formula:

Any other conductors, other than metallic conductors, which obey Ohm’s Law are described as Ohmic conductors.

Example 2What is the current through an 8Ω toaster when it is operating on 240V?

Answer:

(In this question, 2 physical quantities are given, they are the "240V" and "80Ω". The question doesn't tell what quantites they are. However we can recognise these quantities from its unit. Ω is the unit of resistance whereas V is the unit of potential difference.)

Resistance, R = 80ΩPotential difference, V = 240VCurrent, I = ?

V = IR(240) = I(80)I = 3A

Resistance

The resistance R of a material is defined as the ratio V : I, where V is the potential difference across the material and I is the current flowing in it.

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Unit:

The SI unit of resistance is the ohm (Ω). One ohm is the resistance of a material through which a current of one ampere flows when a potential difference of one volt is maintained.

Resistivity

The resistance R of a given conductor depends on the:

length l,Longer wire - Higher Resistance

cross-sectional area A,Thicker wire - Lower Resistance

temperatureHigher temperature - Higher Resistance

the type of materialcopper has resistance lower than iron

Superconductor

Superconductors are materials where their electrical resistance is exactly zero at some relatively low temperature.

Application of Superconductor

1. Magnetic Resonance Imaging (MRI)2. Magnetic-Levitation Train (MagLev)3. Electric generators

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Resistance, Current and Potential Difference in Series Circuit

Effective Resistance: R = R1 + R2

Current: I1 = I2 = I3

Potential Difference V = V1 + V2

Resistance, Current and Potential Difference in Parallel Circuit

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Effective Resistance: R = (R1 + R2 + R3)-1

Current: I = I1 + I2 + I3

Potential Difference V = V1 = V2 = V3

Example 1What is the effective resistance of the connection shown in the picture below?

a. b.

Answer:

a. Effective resistance, R = 2 + 3 + 6 = 11Ω

b. Effective resistance, R = (1/5 + 1/5)-1 = 2.5 Ω

Example 2Find the resultant resistance of the arrangement below.

a. b.

Answer:

a. Effective resistance = 3 + (1/2 + 1/2)-1 = 4Ω

b.

Card 3: Current in Series Circuit

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Current in Series Circuit

The current flow into a resistor = the current flow inside the resistor = the current flows out from the resistor (I1 = I2 = I3)

In a series circuit, the current at any points of the circuit is the same.

Current in Paralle Circuit

The current flow into a parallel circuit is equal to the sum of the current in each branches of the circuit. (I = I1 + I2)

Example:

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If the resistance of the 2 resistors is the same, current will be divided equally to both of the resistor.

Example 3In each of the diagrams below, find the reading of the ammeter.

a. b.

Answer:

a. In a series circuit, the current at any points of the circuit is the same. Therefore, the reading of the ammeter is also 0.5A.

b. Reading of the ammeter, I = 6A - 2A = 4A

Example 4

In the diagram above,

a. find the reading of the ammeter. b. find the current flows through each of the resistors.

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Answer:

a. Resistance of the (whole) circuit = 2 + 4 = 6ΩPotential difference across the whole circuit, V = 12VCurrent, I = ?

V = IR(12) = I(6)I = 2A

Reading of the ammeter = 2A

b.Since in a series circuit, the current at any points of the circuit is the same. Therefore, the current flows through each of the resistors is also 2A.

Potential Difference in Series Circuit

The sum of the potential difference across individual resistor in between 2 points in a series circuit is equal to the potential difference across the two point.

V = V1 + V2

Example

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Potential Difference in Parallel Circuit

The potential difference across all the resistor in a parallel circuit is the same.

V = V1 = V2

Example

Example 5

Find the reading of the given voltmeter(s) in the diagrams below

a. b.

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Asnwer:

a. Reading of the voltmeter, V2 = 12 - 7 = 5V

b. The potential difference across all the resistor in a parallel circuit is the same. Therefore, the reading of the voltmeter V1 is also 5V

Example 6

Find the potential difference across each of the resistors in the diagram above.

Answer:

The potential difference across the whole circuit = 12V, but the potential across the 2 resistor R1 and R2 are unknown. In order to find the potential difference across the resostors, we need to find current passing through the resistors.

V = 12V, R = 6Ω, I = ?

V = IR(12) = I(6)I = 2A

For resistor R1,R = 2Ω, I = 2A, V = ?

V = IRV = (2)(2) = 4V

For resistor R2,R = 4Ω, I = 2A, V = ?

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V = IRV = (2)(4) = 8V

The potential difference across the resistors R1 and R2 are 4V and 8V respectively.Card 7: Potential Difference and E.M.F

Potential Difference and E.M.F

If we assume that there is no internal resistance in the cell, the potential difference across the cell is equal to the e.m.f. of the cell.

Potential Change in a Series Circuit

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V1 = V2 = V5

V3 + V4 = V5

Potential Change in a Parallel Circuit

V1 = V2 = V3 = V4

Example 7Find the reading of the voltmeter in each of the circuit below.

a. c.

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b. d.

Answer:

a. Reading of the volmeter = e.m.f. = 3V

b. Reading of the volmeter = e.m.f. = 3V

c. Reading of the volmeter = e.m.f. = 3V

d. Reading of the volmeter = e.m.f. = 3V

Electromotive Force

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.

Unit:

The unit of e.m.f. is JC-1 or V (Volt)

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Formula of Electromotive Force

Comparing E.M.F. and otential Difference

Electromotive Force Potential Difference

Similarities: Have same unit (Volt)

Can be measured by Voltmeter

DefinitionThe 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.

DefinitionThe 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

Internal resistance

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

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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).

If the internal resistance of the cell is ignored, the terminal potential difference is equal to the e.m.f.

Formulae of Electromotive Force and Internal Resistance

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Finding E.M.F and Internal Resistance - The Open Circuit Method

In open circuit ( when the switch is off), the voltmeter shows the reading of the e.m.f.

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.

Finding E.M.F and Internal Resistance - Linear Graph Method

Gradient od the grapf, m = - internal resistanceY intercept of the graph, c = e.m.f.

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Electrical Energy

From the definition of potential difference, the electric work is given by the formula:

W = QV

(W = Work done; Q = Charge; V = Voltage)

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

Electrical Power

1. The electrical 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.

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Formulae of Electrical Power

Resistance and Power

In a series circuit, the higher the resistance of a resistor, the higher the power of the resistor.

In a parallel circuit, the higher the resistance of a resistor, the lower the power of the resistor.

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Sum of Power

The effective power in a series circuit is equal to the sum of the power of each resistor in the circuit.

P = PR1 + PR2

Sum of power in a Parallel Circuit

The effective power in a parallel circuit is also equal to the sum of the power of each resistor in the circuit.

P = PR1 + PR2

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Calculating The Cost Of Electricity Consumption

The cost of electricity consumption is based on the number of kilowatt-hours (kWh) of electrical energy used. The kilowatt-hours are sometimes known as the domestic units of electricity.

Formula

Ferromagnatic Material

A magnet can attract certain type of metal.

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

Magnetic Field

A magnetic field is a region in the surrounding of a magnet which a magnetic material experiences a detectable force.

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Magnetic Field Line

The magnetic filed of a magnet is represented by the magnetic field line.

The closer the field line, the stronger the field. Magnetic field A is stronger than magnetic field B because the line in magnetic field A is closer.

The magnetic field line flowing out from the North pole and flowing into the South pole.

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