FORM TWO PHYSICS STUDY NOTES TOPIC 1-2

TOPIC 1: STATIC ELECTRICITY

Concept of Static Electricity

The Concept of Static Electricity

Explain the concept of static electricity

Static electricity refers to the electric charges stored on a conductor.

The Orign of Charges

Explain the origin of charges

When a plastic pen is rubbed with a cloth, it acquires the property of attracting small bits of paper or light objects. In this case, the plastic pen is said to be electrified.

Electrification by rubbing was observed a long time ago by ancient Greeks. After the discovery of electricity, things were grouped into two groups, electrics and non-electrics. Electrics refer to things which are readily electrified while non-electrics are reverse of the former.

The two Types of Charges

Identify the two types of charges

There are two types of charge:

1. positive charge
2. negative charge

Identification of charge

Suspend a polythene rod A rubbed with fur. Bring another polythene rod B rubbed with fur up to the rod A. Take a plastic rod and rub it with fur. Bring the plastic rod to up to the suspended rod A. Repeat the exercise with acetate and glass rod rubbed with silk cloth.

Observation

An electrified polythene rod repels another electrified polythene rod. An acetate rod rubbed with silk repels another acetate rod rubbed with silk cloth but it attracts a plastic rod rubbed with fur.

Explanation

Polythene and plastic when rubbed with fur becomes electrified with the same kind of electricity known as negative electricity (charge).

Acetate and glass when rubbed with silk cloth becomes electrified with the same kind of electricity called positive electricity(charge).

Charging is the process of electrifying a body.

A positively charged body carries positive charges and a negatively charged body carries negative charges.The symbols used for positive and negative charges are + and – respectively.

The Fundamental Law of Static Electricity

State the fundamental law of static electricity

The Fundamental law of electrostatic charges states that:“Like charges repel each other while unlike charges attract each other”

Charging Bodies Using Different Methods

Charge bodies using different methods

In order to understand the process of charging we have to understand the structure of bodies or things. All bodies are made up of extremely small, indestructible bits of matter called atoms.

An atom consists of a nucleus surrounded by electrons. The nucleus consists of proton and neutron.The protons are positively charged while electrons are negatively charged and the neutrons are neutral.

The whole atom is electrically neutral because it contain equal number of protons and electrons.

The following are the methods of charging;

1. Rubbing
2. Induction
3. Contact

Charging by rubbing

A polythene rod rubbed with fur becomes negatively charged.Rubbing results in the transfer of electrons from fur to the polythene rod.

Fur becomes positively charged because some of its electrons are transferred to the polythene rod.The polythene gains excess electrons and hence it becomes negatively charged.

Note:It is only the electrons in matter which can be transferred by rubbing.

Charging by induction

A charged polythene rod is held near uncharged copper rod suspended from a cotton thread.

The electrons of the copper rod are repelled by the negatively charged polythene rod.Hence the electrons move to the far side of the copper leaving behind a net positive charge on the side facing the polythene rod.

Touch the copper rod with your finger when the charged rod is still in position. The electrons from copper rod flow through your body to the earth. Leaving it with a net positive charge. Remove the finger from the copper rod and finally remove the charged polythene rod.

The rod has therefore been positively charged by electrostatic induction.The charges that appear on the copper rod are called induced charges.

Charging by contact

A charged body (eg; positively charged metal can) is brought in contact with uncharged body B.

Detection of Charges

The Structure of a Gold-leaf Electroscope

Describe the structure of a gold-leaf electroscope

The instrument used to detect the presence of electric charges is called gold leaf electroscope. It consists of an insulated brass rod with two pieces of thin gold foil at one end and a brass cap at the other end.

When the brass cap is touched with a charged object the leaves of the electroscope spread out. This is because the charge on the object is conducted through the brass cap and the brass rod to the leaves.

As they received the same kind of charge, the leaves repel each other and thus spread apart, this is charging by contact.

If you touch the brass cap with your finger, the charge is transferred through your body to the earth and the leaves of the electroscope then collapse together.

Function of an electroscope

1. Testing for the sign of the charge on the body.
2. Identifying the insulating properties of materials.
3. Detecting the presence of charge on a body.

The Sign of Charges

Determine the sign of charges

The true sign on a body has to be determined before use; the instrument that can be used to determine the presence of charge is called an electrophorus.

An electrophorus consists of a circular slab of insulating material (polythene) together with a brass disc (conductor) on an insulating handle.

An electrophorus works by electrostatic insulation and hence can be used to generate positive charges from single negative charges. The charge produced on the insulating slab is negative. The top disc is then placed on it. Since the surface is only in contact at relatively few points, a positive charge is induced on the lower surface and corresponding negative charge is produced on its top surface.

The top of the upper disc is then touched briefly using a finger, hereby carrying away the negative charge to the earth; this is called EARTHING.

Steps of Charging and Discharging of a Gold-leaf Electroscope

Identify steps of charging and discharging of a gold-leaf electroscope

The polythene slab is charged negative by rubbing it with fur. The brass disc is then placed on top of the slab so that the two charges become induced onto respective materials.

Note:Contact does not negatively charge the disc because it is not flat and makes contact with the slab at a few points only. When the brass disc is touched with a finger, electrons on the upper surface are repelled to the earth.

There is a force of attraction between the metal disc and the base. A spark (electric energy) is normally produced upon their separation. This spark can be used for lighting gas burners in laboratory.

The electrophorus can now be used to charge a gold leaf electroscope.

It can be used to charge a gold leaf electroscope by:

1. Contact
2. Induction

By contact

Here a positively charged electrophorus is made to touch the brass cap of the gold-leaf electroscope. The leaf of the gold-leaf electroscope diverges.

When a charged electrophorus is brought into contact with the electroscope, the latter gets charged and the leaves diverge. It acquires a negative charge. This is determined using the charged rods. When a positively charged glass rod is brought near the cap. It causes the leaf to collapse.

By induction

Induction- is the transfer of opposite effects from one body to another without contact.

In order to obtain a charge of a given sign, the inducing charge must be of an opposite charge. If charge is placed on an insulator at a given location the excess charge will remain at the initial location. The particles of the insulator do not permit the free flow of electrons. Charge present in an insulator or conductor.

Discharging a gold leaf electroscope

Having charged a gold leaf electroscope by contact and induction, the same can be discharged effectively through induction.

If while the electroscope is being charged by induction you touch the brass cap, electrons will leave the electroscope through your hand and onto the ground. If the charged metal rod is removed, the electroscope will remain charged. The charge remaining on the electroscope will be the opposite of the charge on the rod.

If a negatively charged object is now brought near the brass cap electrons in the brass cap are repelled and moved down to the leaves. This cancels the positive charge. With no net charge, the leave collapse back together.

If the object is removed, the electrons return to the metal cap leaving the leaves of the electroscope with a net positive charge again and they separate.

Conductors and Insulators

Difference between a Conductor and Insulator

Distinguish between a conductor and insulator

Conductors

Are bodies, which readily allow electric charge in motion to flow through them

OR

Are materials that permit some electrons to flow freely from atom to atom within the materials examples are copper, steel, iron, silver and gold.

When there is excess of positive or negative charge on an object made of a conducting material, the conduction electrons will move to minimise the repulsive force.

Insulators

These are bodies, which do not allow electric charges to flow through it. Insulators on the other hand do not allow their electrons to flow freely from at atom to atom; this is because the electrons in their atoms move around their nuclei in various equal magnitudes to the charge on the protons. The electrons are also firmly attracted to the nucleus hence bound to these atoms.

Capacitors

Capacitor is a device which is used for the storage of charges consisting of two conductors, parallel-nearly separated by air or any other dielectric.Dielectric is an insulating medium used between plates of a capacitor.

Mode of Action of a Capacitance

Explain mode of action of a capacitance

Consider two unequal metal cans which were made to stand on the caps of two identical electroscopes.These cans are given equal charges of Q units from an electrophorus disc. The charged disc is lowered inside a can until it touches the bottom. In this way the whole of the charge is given up to the can and goes to the outside.

It will be noticed that the leaf divergence is greater for the small can, showing that it has acquired higher potential than the larger can.In this case, the larger can is said to have a larger capacitance while the smaller can has a lower capacitance.When the two cans are joined by a wire electricity flows from the smaller can to the larger can until potentials are equalized.

The Action of a Capacitor

Explain the action of a capacitor

The positive charge on A induces an equal and opposite charges on opposite sides of B. These induced charges will respectively raise and lower the potential of all points in their neighborhood and in particular they will affect the potential of plate A.

As far as A is connected , however the negative induced charge will have the greater effect. The net result is is that the potential of A is slightly reduced.

B is next earthed either by touching it with a finger or by connecting it to the nearest cold-water pipe. Immediately the leaf shows a great decrease in divergence. This implies a big decrease in potential, and hence a big increase in capacitance of A.The presence of the earthed plate B results in a very large increase in the capacitance of A.

Construction of an Air-filled Capacitor

Describe the construction of an air-filled capacitor

This constitute two parallel metal plates with air band between them.A flat metal A is set up vertically on insulating legs and is connected to a gold leaf electroscope by means of a wire.

The plate is then given a positive charge by induction with a negatively charged ebonite rod. The divergence of the leaf indicates the potential of the plate.A second insulated plate B is now brought up slowly into a position parallel to A.

When B is very close to A but not touching it, it will be noticed that the leaf divergence decreases very slightly.We conclude from this that the potential of A has been decreased by the presence of B, and hence its capacitance has increased slightly.

Equivalence Capacitance of a Combination of Capacitors

Determine equivalence capacitance of a combination of capacitors

Factors affecting the capacitance of a parallel-plate capacitor.

There are three factors which affect the capacitance of a parallel-plate capacitor, namely;

1. Area of plates
2. Distance apart of the plates.
3. Dielectric between the plates.

Relative permeability (dielectric constant) of a medium

Relative permeability is the ratio of the capacitance of a given capacitor with the medium as dielectric to the capacitance of the capacitor with a vacuum as the dielectric.

It has no units since it is a ration of similar quantities.Paraffin wax has a relative permeability of about 2 while that of mica is about 8.

Charge Distribution Along the Surface of a Conductor

Charge on a Conductor Reside on its Outer Surface

Recognise that charge on a conductor reside on its outer surface

Usually, charges are distributed on the outer surface of conductors of different shapes.

Investigating surface distribution of a charge on conductors

• A proof plane is pressed into contact with the surface at various places of the conductor.
• The charges on the proof plane are then transferred to the electroscope.
• The divergence of the leaf will give a rough measure of the amount of charge transferred and hence surface density of the charge.

Charge on a Conductor is Concentrated on Sharply Curved Surfaces

Show that charge on a conductor is concentrated on sharply curved surfaces

So far we have considered excess charges on a smooth, symmetrical conductor surface. What happens if a conductor has sharp corners or is pointed? Excess charges on a nonuniform conductor become concentrated at the sharpest points. Additionally, excess charge may move on or off the conductor at the sharpest points.

To see how and why this happens, consider the charged conductor. The electrostatic repulsion of like charges is most effective in moving them apart on the flattest surface, and so they become least concentrated there. This is because the forces between identical pairs of charges at either end of the conductor are identical, but the components of the forces parallel to the surfaces are different. The component parallel to the surface is greatest on the flattest surface and, hence, more effective in moving the charge.

The same effect is produced on a conductor by an externally applied electric field, as seen inFigure(c). Since the field lines must be perpendicular to the surface, more of them are concentrated on the most curved parts.

Excess charge on a nonuniform conductor becomes most concentrated at the location of greatest curvature. (a) The forces between identical pairs of charges at either end of the conductor are identical, but the components of the forces parallel to the surface are different. It isF∥that moves the charges apart once they have reached the surface. (b)F∥is smallest at the more pointed end, the charges are left closer together, producing the electric field shown. (c) An uncharged conductor in an originally uniform electric field is polarized, with the most concentrated charge at its most pointed end.

Lightning Conductor

The Phenomenon of Lightning Conductor

Explain the phenomenon of lightning conductor

Lightning is a gigantic electric spark discharge occurring between two charged clouds or between a cloud and the earth.

Ligthning conductor is a long pointed iron rod with its lower end buried in the earth and the other above the highest part of the building which is used to protect the building from lightning damage.

The Structure and Mode of Action of Lightning Conductor

Describe the structure and mode of action of lightning conductor

Structure of a lightning conductor

It consists of a long thick pointed copper rod with its lower end buried in the earth(earth plate) and the other end reaching above the highest part of the building and ending in several sharp spikes. -It is fixed to the side of the building.

Mode of action of lightning conductor

When a negatively charged thunder-cloudpasses overhead it acts inductively on the conductor,charging the points positively and the earth plate negatively.

The negative charge on the plate is, of course, immediately dissipated into the surrounding earth. At the same time point action occurs at the spikes. Negative ions are attracted to the spikes and becomes discharged by giving up their electrons. These electrons then pass down the conductor and escape to earth.

At the same time positive ions are repelled upwards from the spikes and spread out to form what is called a space charge. This positive space charge, however, has a negligible effect in neutralizing the negative charge on the cloud.

Note:Without the protection of a lightning conductor the lightning usually strikes the highest point, generally a chimney, and the current passes to earth through the path of least resistance. Considerable heat is generated by the passage of the current and sometimes it may set into fire.

A Simple Lighting Conductor

Construct a simple lightning conductor

A simple lightning conductor

TOPIC 2: CURRENT ELECTRICITY

Electric current is the rate of charge flow past a given point in an electric circuit, measured in Coulombs/second which is named Amperes. In most DC electric circuits, it can be assumed that the resistance to current flow is a constant so that the current in the circuit is related to voltage and resistance by Ohm's law. The standard abbreviations for the units are 1 A = 1C/s.

Concept Of Current Electricity

Current Electricity

Define current electricity

Current electricity is a fundamental quantity and is the amount of charge passing a given point in a circuit divided by the time required for the passage of charges.

Electrical current (I) =quantity of charge (Q)/Time (t)

I =Q/t

Q = I.t

Electric current = rate of flow of charge

= (the number of charge carried per second x charge of a single electron)

From this definition the SI unit of an electric current is I =Columbus(C)/Second (s)

I = c/s = A

This unit is commonly known as an Ampere (A). Other units are milliamperes (mA), kilo amperes (KA) and Microampere (mA).

Their equivalents to the ampere are as follows:

1A = 10-3mA

1A= 10-6mA

1KA = 1000A

So when a steady electric current of 1A is flowing in a circuit a coulomb of charge passes a given point of the circuit per second.

An instrument used to measure electric current is called an Ammeter.

In this chapter we shall study the sustained movement of electric charge called electric current. To maintain a steady flow of electricity charge capable of moving and ways of causing them to move. Secondly, there must be a closed path around which the charge moves. This path is known as electric circuit.

A coulomb

This is the quantity of electricity, which passes a given point in circuit in 1 second when a steady current of 1 ampere flows.

In electric current there are flows of electrons through the conductor. Electrons are negatively charged while protons are positively charged. The motion of the charge through the circuit transfers energy from one point to another. This means that the actual directors of an electric current are opposite to the conventional direction.

Uses of current electricity

Current electricity is mainly used for:

1. Cooking
2. Lighting
3. Communication; and
4. Heating among many other uses

Different Sources of Current Electricity in Everyday Life

Identify different sources of current electricity in everyday life

All sources of electric currents work by converting some kind of energy into electrical energy. The two basic sources are:

1. Batteries e.g. Mobile phone battery, car dry cell batteries and also car alternator.
2. Generator

Batteries convert chemical energy into electrical energy. While generators convert mechanical energy into electrical energy.

Other sources of electric energy include water (hydroelectric power), water currents i.e. ocean waves, solar energy and wind energy.

Hydroelectric power is very reliable except in time of severe drought. This is because electricity is generated from water in dams and waterfalls, which depends on rainwater. Turbines are used to generate electricity form falling water.

Solar cells trap and convert solar energy into electric energy. Space ships and satellite use solar cell to convert sun light into electricity.

Simple Electric Circuits

Simple Circuit Components

Identify simple circuit components

An electric circuit contains a source of moving charge (battery or generator), connecting wires made of conducting materials (usually copper metal) and various electrical devices such as bulbs, switches, resistors, ammeters and voltmeters.

Voltmeters measure potential difference in volts. While resisters opposes the flow of current. The circuit may also contain devices for controlling the amount of current. These include:

1. Rheostat
2. Fuse
3. Circuit breakers, as well as devices for measuring current such as ammeters and galvanometers.

The table below shows list of some common circuit component and their purpose.

Circuit device	Purpose
Connecting wire	Carry current from point to point in a circuit.
Wire joined
Wire crossing (can be connected)
Cell	Supplies electrical energy
Battery (4 cells)	Supplies electrical energy
Battery (multiple cells)
Alternating current (AC) supply
Lamp/bulb	Supplies electrical energy
Resistor	Impedes the flow of current
Switch	Open and closes a circuit
Rheostats (variable resistors	Control amount of current. For example the brightness of a lamp)
Galvanometer	Detecting the presence of current
Ammeter	Measures current
Milliammeter
Voltmeter	Measures potential Difference (voltage)
Capacitor	Store charges

Simple Electric Symbols

Identify simple electric symbols

Connecting wire

Wire joined

Wires crossing

Cell

Battery

Battery (multiple cells)

Alternating current (AC) supply

Lamp/bulb

Resistor

Switch

Rheostats (variable resistors)

Galvanometer

Ammeter

Milliammeter

Voltmeter

Capacitor

Potential Difference (P.D)

Potential difference or voltage is a measure of electrical energy.

Potential difference (p.d) between the +ve and –ve terminals of a battery causes a current to flow along any conducting path that links them.

The Concept of Current, Voltage and Resistance

Explain the concept of Current, Voltage and Resistance

CURRENT

An electric current in a material is the passage of charge through the material. In metals free electrons carry charge. In solutions such as sodium chloride it is carried by charged particles known as ions.

Insulators like wood and plastic do not contain charge carriers at all as every electron is firmly fixed onto their atoms. The electrons are not free to move.

The rate of flow of electrons in a material is called electric current. It is measured in amperes (A) using an Ammeter. Connection can damage them. Therefore when connecting the ammeter, the red wire should be connected to the +ve terminal of a battery.

A current of 1A is equivalent to a flow of6.25 x 1018electrons per second and 1 electron has a charge of 1.6x 10-19c.

Current in simple circuit is the same at all points.

Once the circuit is complete, electric charges inside cells and other sources of electric charge are forced out into the circuit.

The electric energy is normally given out as light and heat, as energy goes through the bulb. A car headlamp has about 4A of current passing through it while a small torch uses about 0.2A.

VOLTAGE

When several cells have been joined together, they form a battery. Every cell has a voltage, commonly referred to as potential difference (p.d). This potential difference (p.d) causes the flow of electrons (charges) in a circuit.E.g. A dry cell has a voltage of 1.5v. This voltage is normally marked on the cell.

Voltage is measured by using a voltmeter. The SI unit for voltage is the volt (V). If each coulomb if charge is given 1 joule of potential energy, then the p.d across the terminals of a battery is 1 volt.

The p.d between the ends of a connecting wire is zero since there is almost no loss of potential energy over this section.

P.d across the battery = sum of p.d around a conducting path, whereas voltage provides the driving force to an electric current, this force is always opposed.

RESISTANCE

Is the opposition flow to an electric current. As current flows through the circuit it encounters some opposing force. This force determines the amount of current flowing in an electric device.

The property of conductors that oppose the flow of electric charges depends on the relationship between current and voltage across their ends as discovered by George Ohm. He observed that voltage across a conductor was directly proportional to electric current flowing through it provided that temperature and other physical conditions of the conductor were kept constant.

Hence, V x I

V= IR

R is the constant of proportionality. This constant is called resistance and the above relationship is known as Ohms law.

Resistant (R) = p.d across the conductor/Current through the conductor

Therefore a resistance of 1ohm is obtained when a p.d of 11V cause a current of 1A to flow in a circuit.

name	symbol	conversion	example
milli-ohm	mΩ	1mΩ = 10-3Ω	R0 = 10mΩ
ohm	Ω	-	R1 = 10Ω
kilo-ohm	kΩ	1kΩ = 103Ω	R2 = 2kΩ
mega-ohm	MΩ	1MΩ = 106Ω	R3 = 5MΩ

A resistor

Is a device especially designed to offer resistance to the flow of an electric current, Resistors include rheostats (variable resistor) and fixed resistors.

Ohm's Law

Ohms law states, “At constant temperature and other physical factors, the potential difference across the end is directly proportional to the current passing through a conductor (wire).”

A graphical representation of Ohm's law. The graph of voltage against current

The gradient of the particular graph represents resistance. This is constant for a particular wire or conductors. Doubling the voltage would double the current; a graph of this kind passes through the origin.

FACTORS THAT AFFECT THE RESISTANCE OF A CONDUCTOR

The resistance of a conductor is affected by the following factors:

Length of the conductor

The longer the wire, the higher the resistance, short lengths of wire produce resistors of low resistance while long lengths of the same wire are good for high – value resistance.

Temperature

An increase in temperature of a conductor means an increase in its resistance and vice versa. This is important in resistance thermometers. The resistance of metal conductor increases with increase in temperature.

Types of material

The conducting ability of the material has to be considered. A chrome wire has more resistance than a copper wire of the same dimension. That is why copper is mostly used for connecting wire.

Cross – sectional area

A thin wire has more resistance than a thick conductor. The filament of a bulb is made of very thin tang stem wire. It therefore has a high melting point.

With all other factors being equal, a long wire has more resistance than a short wire and thin wire has more resistance than a thick one. Therefore resistance of a conductor varies depending on the current flow.

The SI Units of Current, Voltage and Resistance

State the SI units of Current, Voltage and Resistance

Current

The rate of flow of electrons in a material is called electric current. It is measured in amperes (A) using an Ammeter. The SI unit for current is ampere.

Voltage

Voltage is measured by using a voltmeter. The SI unit for voltage is the volt (V)

Resistance

Resistant (R) = p.d across the conductor/Current through the conductor. The SI unit for resistance is Ohm.

Connecting Simple Electric Circuits

Connect simple electric circuits

CONSTRUCTION OF SIMPLE ELECTRIC CIRCUITS

Consider a circuit consisting of a battery, a switch and 2 bulbs.

When the switch is closed, current flows through the wires and the bulbs light up. The circuit is said to be complete. When the switch is opened, no current flows through the wire, as the path carrying current is broken. The circuit is said to be incomplete.

If we want to be able to control the brightness of the lamp, we include a rheostat into the circuit.

In a circuit an ammeter is always connected in series with the battery. Current has to pass through the ammeter if it is to be measured correctly.

Unlike an ammeter, a voltmeter must be connected in parallel with component so as to measure the voltage drop across it. The figures show a simple electric circuit in which the ammeter and voltmeter are connected in series and parallel respectively.

As already learnt, resistance is the ratio of the potential difference across the ends of the conductor,a very good conductor will have 0 resistance.

Resistance of resistor R could be calculated using the formula:- R = V/I

R = V/I

Not that the rheostat (variable resistor) moves, it varies with the length of the conductor being used.

Example 1

A battery of 5V has a resistance wire of 20Ω connected to it. Calculate the current in the circuit.

Solution;

I = V/R = 5V/20Ω

I = 0.25A

Therefore,

Current in the circuit = 0.25A

Example 2

Calculate the reading of the Voltmeter P and the ammeter Q in the electric circuit below.

Solution:

Being a single loop circuit, current is the same at all points.

Q = 3A

Sum of p.d in external circuit = p.d across battery

3V + P = 13V

P = 10V

Therefore:

Q = 3A and Voltmeter P = 10V

Note: for a single loop or simple circuit.

1. Current is the same at all points around the circuit
2. The sum of the potential differences around a conducting path from one battery terminal to the other terminal within the circuit is the same as the p.d across the battery.

Electric Current and Voltage

Measure electric current and voltage

MEASUREMENT OF ELECTRIC CURRENT

Since we cannot see electric current to measure it, we must observe some of its visible effects, like deflection of pointers.

Beside an ammeter, an electric current is measured using Milliammeter and microammeters. These devices are normally connected in series with the source of current e.g. circuit with a galvanometer connected in series.

Galvanometer in series

Galvanometer can only measure very small current of a few hundred microamperes. To measure large currents a resistor is added to make current flow through it and a very small amount of current flows to the galvanometer. This combination is called an ammeter.

On the other hand voltage is measured depending on the amount of current passing through the circuit. In Ohmic device it is given as V^I.

Simple Electric Circuits

Analyse simple electric circuits

Combination of resistors

There are two main methods of connecting circuit components, in series or in parallel. Resistors can be connected either in series or in parallel depending on the desired output.

Series combination

In series arrangement the resistors are connected end to end.

In a simple circuit

V = V1 + V2 or V- (V1 + v2)= 0

This means that the sum of the p.d across the resistors is the same as the p.d across the battery.

Current is the same at all points around the circuit.

Resistors connected in series

Parallel combination

Resistors are connected across two common points in a parallel arrangement.

Note; Potential difference is from a single source and so is the same for all the branches. However the current is different in each branch.

From Ohm's law;

Note:

When bulbs have to be powered by a single source of electric current, the bulbs are connected in parallel. This is practiced in car and home lighting system.

The advantage of parallel arrangement over series arrangement is that:

1. The full p.d of source is applied across each bulb irrespective of the number of bulbs.
2. Switching one bulb on and off does not affect the others.

Example 3

consider the figure below:

Given that the p.d a cross the cell is 24V, calculate the p.d across the 4Ω and 6Ω.

Solution;

Total resistance in the circuit = 4Ω + 6Ω= 10Ω

Using Ohm’s law. I = V/R,

Current in the circuit = 24V/10Ω= 2.4A

This implies the 2.4A passed through the 4Ω resistor.

The pd across it can be obtained through V=IR

p.d = 2.4A x 4N = 9.6V

Note that the p.d across two resistors adds up to the battery p.d.

p.d across the 6Ω = (24-9.6) V

= 14.4V

Therefore,

P.d across the 6Ω =14.4V