Electricity

Electricity

• The branch of physics which deals with the study of charge in motion/flow of charge is called electricity.

• A stream of electrons moving through a conductor constitutes an electric current.

• It is a form of energy for a variety uses in homes, school, hospital, industries and so on.

Electric Charge

• It is the property associated with a matter due to/by which it attract or repels other material.

• Its SI unit is coulomb (C).

• It is denoted by `Q`.

Properties of charges

• It is a scalar quantity

• Like charges repel and unlike charges attract each other.

• Charges can neither be created nor be destroyed and it remains constant.

There are two types of charges

1. Positive charge

Magnitude of charge on one proton is +1.6×10̄  ̄¹⁹C.

2. Negative charge

Magnitude of charge on one electron is -1.6×10  ̄¹⁹C

Quantization of charge

The quantization of charge is the property by virtue of which every charge exists only in discrete values.

Q = ne.

Where, n is number of electron

e is charge on electron

Q is charge.

Electric current

• The amount of charge flowing through a particular area in unit time is called electric current.

Or

• The rate of flow of charge is called electric current.

• If a net charge Q, flows across any cross-section of a conductor in time t, then the current I, through the cross-section is-

Current=Amount of Charge/Time

I = Q/t

• The SI unit of electric current is Amphere (A).

• One ampere is constituted by the flow of one coulomb of charge per second, i.e  1A=1C/1s.

• 1 Columb of charge contains 6 × 10¹⁸ electrons.

• Small quantities of current are expressed in milliampere (1 mA = 10  ̄³ A) or in microampere (1 µA = 10  ̄⁶A).

• Current is measured by an instrument called ammeter.

• Conventionally, the direction of electric current is taken as opposite to the direction of the flow of electrons.

Electric potential

• Electric potential at a point in an electric field is defined as the work done required in moving a unit positive charge from infinity to that point.

• It is denoted by V.

• It's SI unit is Volt.

V = W/Q 

Electric potential difference

• Electric potential difference between two point inside an electric field is defined as the amount of work done in moving a unit positive charge from one point another point is called the potential difference between those points.

Potential difference (V) between two points = Work done (W)/Charge (Q)

Voltage=∆V = Wᴀʙ/Q 

• The SI unit of electric potential difference is volt (V).

• SI unit is joul/coulomb.

One Volt

• One volt is the potential difference between two points in a current carrying conductor

when 1 joule of work is done to move a charge of 1 coulomb from one point to the other.

• Therefore, 1 volt = 1 joule/1 coulomb

1 V = 1 J/C  ̄¹.

• Potential difference is measured by an instrument called Voltmeter.

• For flow of charges/electrons in a conducting metallic wire, there is a difference of electric pressure called the potential difference along the conductor.

Electric Circuit and Circuit Diagram

Electric Circuit

• A Closed and continuous path through which electric current flows is known as electric circuit.

Circuit diagram

• It is the pictorial representation of a circuit in which different electrical components of the circuit are presented by their symbols.

Or

A diagram which indicates how different components in a circuit have been connected by using the electrical symbols for the components is called the circuit diagram.

• An electric circuit comprises/consist a cell (or a battery), a plug key, connecting wires, electric bulb, an ammeter, voltmeter and other electrical components.

• The electric current flows in the circuit from the positive terminal of the cell to the negative terminal of the cell through circuit.

• The actual flow of electrons is from negative terminal to positive terminal of a cell.

• Conventionally, in an electric circuit the

direction of electric current is taken as opposite to the direction of the flow of electrons.

Switch

• A switch makes a conducting link between the cell and the bulb. 

• If the circuit is broken anywhere (or the switch of the torch is turned off), the current stops flowing and the bulb does not glow.

• In a torch, the cells or a battery provide

flow of charges or an electric current through the torch bulb to glow. 

• The torch gives light only when its switch is on.

Ammeter:

• An instrument called ammeter measures electric

current in a circuit.

• It is always connected in series in a circuit through which the current is to be measured.

Voltmeter:

• Potential difference is measured by voltmeter.

• It is always connected in parallel.

Rheostat

A component used to regulate current without changing the voltage source is called variable resistance. 

  

In an electric circuit, a device called rheostat is often used to change the resistance in the circuit.

Symbols used to represent some of the most

commonly used electrical components are given below:

Ohm's Law

• This law gives the relationship between the potential difference across a conductor and the current through it.

• According to this law " At constant temperature, the electric current flowing in/through a conductor is directly proportional to the potential difference applied across the ends of the conductor".

• If I is the current flowing through a conductor and V is the potential difference (or voltage) across its ends, then according to Ohm’s law :

V ∝ I

V = IR

Where, R is a constant for the given metallic wire/conductor at a given temperature and is called its resistance. 

Resistance:

• The property of a conductor due to which it opposes/resist the flow of current/charge through it is called resistance.

• it controls the magnitude of the current.

• The ratio of potential difference applied between the ends of a conductor and the current flowing through it is a constant quantity called resistance.

R = V/I

• The current through a resistor is inversely proportional to its resistance.

•  If the resistance is doubled, the current gets halved, and if the resistance is halved, the current gets doubled.

• It is a scalar quantity.

• Its SI unit is ohm or volt/Ampere and represented by the Greek letter Ω.

1 Ohm

If the potential difference across the two ends of a conductor is 1 V and the current through it is 1 A, then the resistance R, of the conductor

1 volt is 1 Ω.

• The motion of electrons through a conductor is retarded by its resistance. 

• Those substances which have very low electrical resistance are called good conductors.

• Those substances which have comparatively high/appreciable electrical resistance, are called resistors.

 

• Those substances which have infinitely high electrical resistance are called insulators/poor conductor.

V-I Characteristics Curve/Graph

If a graph is drawn between the potential difference readings (V) and the corresponding current values (I), the graph is found to be a straight line passing through the origin. Thus, V/I is a constant ratio.

Factors Affecting Resistance of a conductor.

• The electrical resistance of a conductor (or a wire) depends on the following factors : 

(i) Length of the conductor.

• The resistance of a uniform metallic conductor is directly proportional to its length. 

R ∝ l (where l is the length of conductor)

• i.e On increasing the length of a wire, its resistance increases; and on decreasing the length of the wire, its resistance decreases.

• When the length of a wire is doubled, its resistance also gets doubled and if the length of a wire is halved, then its resistance also gets halved.

• Long wire has more resistance and a short wire has less resistance.

(ii) Area of cross-section of the conductor (or thickness of the conductor).

• The resistance of a conductor is inversely proportional to its area of cross-section.

R ∝ 1/A

• When the area of cross-section of a wire is doubled, its resistance gets halved and if the area of crosssection of wire is halved, then its resistance will get doubled. 

• This means that a thick wire has less resistance, and a thin wire has more resistance.

(iii) Nature of the material of the conductor

• If we take two similar wires, having equal lengths and diameters, of copper metal and nichrome alloy, we will find that the resistance of nichrome wire is about 60 times more than that of the copper wire.

• This shows that the resistance of a conductor depends on the nature of the material of the conductor.

Resistivity:

• The Resistance of a uniform metallic conductor is directly proportional to its length (l) and inversely proportional to the area of cross-section (A). That is,

R ∝ l .........i

R ∝ 1/A ...........ii

Combining Eqn i and ii, we get

R ∝ l/A

R = ρl/A

where ρ (rho) is a constant of proportionality and is called the electrical resistivity of the material of the conductor. 

• Resistivity is the resistance of a conductor having unit lenght and unit areal of cross section.

• The SI unit of resistivity is Ω m. 

RA/l= ρ

Ωm²/m = ρ

ρ =Ω m.

• It is a characteristic property of the material. 

• Resistivity of metallic conductor does not depends on the lenght or thickness of wire, it depends on the nature of the substance and temperature.

• The metals and alloys have very low resistivity in the range of 10  ̄⁸ Ω m to 10  ̄⁶ Ω m so they are good conductors of electricity. 

• Insulators like rubber and glass have resistivity of the order of 10¹² to 10¹⁷ Ω m. 

• Both the resistance and resistivity of a material vary with temperature.

(iv) Temperature of the conductor.

• The resistance of all pure metals increases on raising the temperature; and decreases on lowering the temperature.

Difference between resistance and resistivity

Combination Of Resistances (Or Resistors)

The resistances can be combined in two ways :

i) In Series

• When two (or more) resistances are connected end to end consecutively, they are said to be connected in series.

• The combined resistance of any number of resistances connected in series is equal to the sum of the individual resistances.

Rs = R₁ + R₂ + R₃.....

• If resistances are connected in series then equivalent resistance is greater than the resistance of individual resistance.

• If we want to increase the total resistance, then the individual resistances are connected in series.

Division of Current and Voltage in Series

• When a number of resistances are connected in series, then the same current flows through each resistance. i.e I remains same in series.

• When a number of resistances connected in series are joined to the terminals of a battery, then each resistance has a different potential difference across its ends i.e V divides in series.

Deriving Series Formula

VT = V₁ + V₂ + V₃.....

RT = IR₁ + IR₂ + IR₃.....

IRT = I(R₁ + R₂ + R₃.....)

RT = R₁ + R₂ + R₃..........

ii) In Parallel

• When two (or more) resistances are connected between the same two points, they are said to be connected in parallel.

• The reciprocal of the combined resistance of a number of resistances connected in parallel is equal to the sum of the reciprocals of all the individual resistances.

1/Rp = 1/R₁ + 2/R₂ + 3/R₃.......

• When a number of resistances are connected in parallel then their combined resistance is less than the smallest individual resistance.

• If we want to decrease the resistance, then the individual resistances are connected in parallel.

Division of Current and Voltage in Parallel

• When a number of resistances are connected in parallel, then the potential difference across each resistance is the same which is equal to the voltage of the battery applied i.e V remains same in parallel.

• When a number of resistances connected in parallel are joined to the two terminals of a battery, then different amounts of current flow through each resistance i.e I divides in parallel.

Deriving Parallel Formula

IT = I₁ + I₂ + I₃.....     (I = V/R)

V/RT = V/R₁ + V/R₂ + V/R₃.......

V/RT = V(1/R₁ + 2/R₂ + 3/R₃.......)

1/RT = 1/R₁ + 2/R₂ + 3/R₃.......

Disadvantages of Series Circuits 

1. If one electrical appliance/components stops working due to some defect, then none of the components works.

2. All the electrical appliances have only one switch due to which they cannot be turned on or off separately. 

3. The appliances do not get the same voltage (220 V) as that of the power supply line.

4. The overall resistance of the circuit increases too much due to which the current from the power supply is low.

Advantages of Parallel Circuits

1. If one electrical appliance stops working due to some defect, then all other appliances keep working normally. 

2. Each electrical appliance has its own switch due to which it can be turned on or turned off independently, without affecting other appliances.

3. Each electrical appliance gets the same voltage (220 V) as that of the power supply line.

4. In the parallel connection of electrical appliances, the overall resistance of the household circuit is reduced due to which the current from the power supply is high.

Heating effect of electric current

• In an electric circuit, to maintain the flow of current, the source continuously has to provide the energy. 

• Some part of this supplied energy helps in maintaining the current, rest of it may be descipated in the form of heat. This is known as Heating effect of electric current.

• When an electric current is passed through a high resistance wire or a conductor, the resistance wire becomes very hot and produces heat.

• In this effect electrical energy is converted into heat energy when an electric current flows through a resistance wire.

Joule’s law of heating

This law states that " Heat produced in a resistor/wire/conductor is directly proportional to the square of amount of current flowing, resistance of the conductor/wire, time period (t) for which current is passed.

H ∝ I² .......i

H ∝ R ........ii

H ∝ T .........iii

Combination the above equations we get,

H = I²RT

Proof of Jouls Law:

• Consider a current I flowing through a resistor of resistance R. 

• Let the potential difference across it be V and t be the time during which a charge Q flows across. 

• The work done in moving the charge Q through a potential difference is_

V = W/Q

W = QV .....i

Current,  I = Q/t

Q = It ......ii

Potential difference,  V = IR .......iii

Putting the values of Q and V from eqn ii and iii in eqn i we get,

W = (It) × (IR)

H = I²RT

Practical Applications of Heating Effect of Electric Current

i. It is utilised in the working of appliance such as electric iron, electric kitten , electric toaster, electric oven.

ii. It is used to produce light ( Electric Bulb): 

• It has a filament made of tungsten. 

• Due to high Resistivity and high melting point of tungsten (3380°C), when voltage is applied across the filamen,t it gets heated to a very high temperature, It then becomes very hot and starts radiating/emits heat and light.

iii. It is used as fuse (safety device) in household/electric circuits. 

• It consists of piece of wire made up of alloy (lead and tin) which has appropriate melting point. 

• When the current flowing through the circuit exceeds the safe limit, the temperature of fuse wire increases, this fuse melts the fuse wire and breaks the circuit.

• It helps to protect the other circuit and appliances from hazard caused by current.

Electric Power