Current Electricity

CURRENT ELECTRICITY

Current electricity is the rate at which an electricity source will make charges to flow or pass a certain point in a conductor or in an electric circuit.

This means that, when electrical devices 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:

Cooking
Lighting
Communication; and
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:

Batteries e.g. Mobile phone battery, car dry cell batteries and also car alternator.
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:

Rheostat
Fuse
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	Measures current
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.

Current is the same at all points around the circuit
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

Resistors can be connected either in series or parallel depending on the magnitude of effective resistance required. Series connection gives a bigger value of effective resistance and the parallel connection gives small value of effective resistance.

RESISTORS IN SERIES

By connecting resistors in series, when the switch 'S' is closed, the current 'I' which flows through the circuit flows through each resistor.
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Total resistance between points A and B which is commonly referred to as equivalent resistance (Req) will produce a potential difference in the circuit given by ohm’s law as;

V=IReq

The voltage across each resistor in the circuit is given by V1 =IR1 and V2 =IR2

The sum of the voltage drops equal to the potential difference in the circuit (i.e. potential difference between (A and B)

Total voltage = V1 + V2

... VT = V1 + V2

Total voltage = V1 + V2

Since V = IR, V1 = IR1 and V2 = IR2

IRT = IR1 + IR2

IRT =I (R1 + R2 )

RT = R1 + R2

RESISTORS IN PARALLEL

In the figure below I is the current in the main circuit. On the other hand I1 and I2 are current through individual resistors R1 and R2.

The sum of all currents through the resistors which are connected in parallel gives the value of current equal to the main circuit.
$C:\thlb\cr\tz\__i__images__i__\HHHHH1.jpg$ .

Therefore, IT = I1 + I2

If RT is the equivalent resistance of the main circuit between A and B, then by Ohm’s law the current is given by;

$C:\thlb\cr\tz\__i__images__i__\i1.jpg$

From IT = I1 + I2

$C:\thlb\cr\tz\__i__images__i__\ii1.jpg$
On diving both sides by V

$C:\thlb\cr\tz\__i__images__i__\iii2.jpg$

Cross multiplication

1(R1R2) = RT (R1 + R2)
$C:\thlb\cr\tz\__i__images__i__\iiii1.jpg$

For two resistors connected in parallel.

EXAMPLES

1.Given that R1= 4Ω and R2= 6Ω, find the equivalent resistance when the resistors are connected.

In parallel

2. In series

Solution

1.Series

$C:\thlb\cr\tz\__i__images__i__\j1.jpg$
RT = R1+R2

RT = 4Ω + 6Ω

RT = 10Ω

2.Parallel

$C:\thlb\cr\tz\__i__images__i__\jj3.jpg$

$C:\thlb\cr\tz\__i__images__i__\jjj1.jpg$

= 2.4Ω

2.Two conductors of resistance 4Ω and 5Ω are connected in series across a 60V supply. Find;

The total resistance
The current in the circuit
The potential difference across each resistor

$C:\thlb\cr\tz\__i__images__i__\k1.jpg$

RT = R1+R2

= 4Ω + 5Ω

= 9Ω
the total resistance = 9Ω

$C:\thlb\cr\tz\__i__images__i__\kk2.jpg$

I = 6.7A

Potential difference across R1

V1 = IR1

V1 = 6.7 x 4 = 26.8v

Potential difference across R2

V2 = IR2

V2 = 6.7 x 5 = 33.5v

Total current = 26.8 + 33.5 = 60A

3.Consider the circuit shown below. What will be the reading on the Ammeter?

Solution

V = 12V

$C:\thlb\cr\tz\__i__images__i__\kkk2.jpg$

$C:\thlb\cr\tz\__i__images__i__\KKKK3.jpg$

RT =2Ω

$C:\thlb\cr\tz\__i__images__i__\l2.jpg$

I = 6A

EXERCISE

1. In a circuit, the amount of charges passing through a point is 9 coulombs in 4.5 seconds. What is the electric current passing at that point?

Solution

Quantity of charges = 9 coulombs

Time = 4.5 sec

Electric current =?
$C:\thlb\cr\tz\__i__images__i__\ll3.jpg$

Electric current = 2coulombs/sec

2. The two resistances 15Ω and 5Ω are connected in series across 20v supply, find;

Total resistance
The total current in the circuit
The current through each resistor

Solution

Data given

R1 = 15Ω

R2 = 5Ω

Voltage = 20v

The total resistance

RT = R1 + R2

= 15Ω + 5Ω

= 20Ω

The total current in a circuit (I)

From V = IR
$C:\thlb\cr\tz\__i__images__i__\LLL2.jpg$

But v = 20v, R = 20Ω

$C:\thlb\cr\tz\__i__images__i__\LLLL1.jpg$
I = 1A

The current through each resistor

$C:\thlb\cr\tz\__i__images__i__\LLLLL1.jpg$

But V = 20V, R1 =15Ω

$C:\thlb\cr\tz\__i__images__i__\M1.jpg$

= 1.3A

$C:\thlb\cr\tz\__i__images__i__\MM1.jpg$

but V = 20 V, R = 5Ω

$C:\thlb\cr\tz\__i__images__i__\MMM1.jpg$

I2 = 4A

ALL TOPICS
NoTes

1...Static Electricity

2...Current electricity

3...Magnetism

4....Equlibrium

5...Simple Machine

6...Motion in a straight line

7...Newton law of motion

8....Temperature

Current Electricity

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