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12. Electricity

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Frictional electricity: The electricity developed by rubbing or friction is called frictional electricity. 

Electric charge: There are two types of electric charge,

1. Positive charge: Charge acquired by a glass rod when rubbed with silk is called positive charge.

2. Negative charge: Charge acquired by a ebonite rod when rubbed with wool is called negative charge. 

• Positive charge is produced due to less electrons. 
• Negative charge produced due to more electrons. 

Fundamental law of electrostatics: 

• Like charges repel each other. 
• Unlike charge attract each other.

Statics electricity: Statics electricity deals with the electric charges at rest. 

Current electricity: current electricity deals with the electric charges in motion. 

Electric Current And Charge:

When the electric charge flows through a conductor, we say that there is an electric current in the conductor.

In other words: An electric current is a flow of a electric charge. 

Electric current is expressed by the amount of charge flowing through a particular area in unit time.

• Electric current flows throught a wire/conductor.
• Electric current is a scalar quantity. 

Flowing/moving of electrons:

The electrons are repelled by the negative charge at the negative terminal of the battery and attracted by the positive charge at the positive terminal. Therefore the electrons drift away from the negative terminal and toward the positive terminal. When electrons reach the positive terminal a chemical reaction transfers them across the battery and back to the negative terminal. 

Conductor:

A substances which allows the passage of electric charge throught it easily, is called conductor. Example: copper, silver, aluminium etc. 

• Good conductors have low resistance to the flow of current.
• Bad conductors have high resistance to the flow of current.  

Insulator: A substance which does not allow electric current to flow through it is called insulator. Example- rubber, plastic ebonite, glass etc. 

Cunductivity: Conductivity is a property of conductor by which it allow the passage electric charge throught it.  

Supercunductivity: Superconductivity is a phenomenon of exactly zero electrical resistance at very low temperature.

Coulomb's law: The force of attraction or repulsion between two point charges are directly proportional to the product (q₁q₂) of the two charges and inversely proportional to the square of the the distance(r) between them. 

Mathematically,

F ∝ q₁q₂          ......................... (i) 

F ∝ 1/ r²          ..........................(ii) 

k is constant value, but the value of K depends on the nature of the medium between the two charges. 

Charges in vacuum of K = 9 × 10⁹ Nm²/C²

Electric Circuit:

A continuous and closed path of an electric current is called an electric circuit.

The flow of the electricity:

Electrons constitute the flow of charge. electric current was considered to be the flow of positive charges and the direction of flow of positive charges was taken to be the direction of 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;

I = Q/t

The SI unit of electric charge is coulomb (C), which is equivalent to the charge contained in nearly 6 × 10¹⁸ electrons.

Coulomb: It is the SI unit of charge, which is equivalent to the charge contained in nearly 6 × 10¹⁸ electrons.

Charge on an electron = -1.6 × 10^-19 coulomb (C).

Charge on a proton = 1.6 × 10^-19 coulomb (C).

Law of conservation of charge: Electric charges can neither be created nor destroyed, they can only be transferred from one body to another body. 

Ampere: It is the SI unit of current. When one coulomb of charge flows in one second it is called one Ampere of current.

1A = 1C/1s;

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

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

Ammeter: It is a device to measure electric current in a circuit. It is always connected in series in a circuit.  

Galvanometer: It is a device to detect current in an electric circuit.

Conventional current: Conventionally, the direction of motion of positive charges is taken as the direction of current. The direction of conventional current is opposite to the flow of electron.  

Direction in which an electric current is considered to flow in a circuit. By convention, the direction is that in which positive-charge carriers would flow - from the positive terminal of a cell to its negative terminal. It is opposite in direction to the flow of electrons. 

Electrostatic potential: 

Electrostatic potential at any point in an electric field is defined as the amount of work done in bringing a unit positive charge of one coulomb from infinity to that point. Its unit is volt. 

Potential Difference:

The electrons move only if there is a difference of electric pressure, this difference in electric pressure is called the potential difference – along the conductor.

• This difference of potential may be produced by a battery, consisting of one or more electric cells.
• The chemical action within a cell generates the potential difference across the terminals of the cell, even when no current is drawn from it.
• When the cell is connected to a conducting circuit element, the potential difference sets the charges in motion in the conductor and produces an electric current. In order to maintain the current in a given electric circuit, the cell has to expend its chemical energy stored in it.

Potential difference between two points: 

the electric potential difference between two points in an electric circuit carrying some current as the work done to move a unit charge from one point to the other.

Or

• The SI unit of electric potential difference is volt (V), named after Alessandro Volta (1745–1827), an Italian physicist.

Voltmeter: 

The potential difference is measured by means of an instrument called
the voltmeter.

One volt potential difference: 

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.

Connection of voltmeter:

The voltmeter is always connected in parallel across the points between which the potential difference is to be measured.

Cells Or Battery: It is a device which helps to maintain the potential difference between two points of conductor. 

Electromotive force (EMF): It is a force applied by cell or battery to produce electric current through a wire. 

Ohm's Law:

The electric current flowing through a metallic wire is directly proportional to the potential difference V, across its ends provided its temperature remains the same. This is called Ohm’s law.

According to this law. 

V ∝ I            or  V = RI 

see this volt-current graph 

if potential difference is increased then electric current also increases.

And if potential difference is decreases then electric current also decreases.

Resistance: 

It is the property of a conductor to resist the flow of charges through it. 

Using ohm law: 

Resistance = Potential difference/Current

• SI units of resistance is Ohm(Ω).
• V/I = R, which is a constant. 

1 Ohm of resistance: 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 is 1 Ω.

• The current through a resistor is inversely proportional to its resistance.
• If the resistance is doubled the current gets halved.
• In many practical cases it is necessary to increase or decrease the current in an electric circuit.

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

Rheostat: It is a device which is often used to change the resistance in the electric circuit. 

Resistor: A conductor having some appreciable resistance is called a resistor.

Some points: 

• Certain components offer an easy path for the flow of electric current while the others resist the flow.
• motion of electrons in an electric circuit constitutes an electric current.
• The electrons, however, are not completely free to move within a
  conductor.
• They are restrained by the attraction of the atoms among which they move.
• motion of electrons through a conductor is retarded by its resistance.

Good conductor: A component of a given size that offers a low
resistance is a good conductor.

Poor conductor: A component of identical size that offers a higher resistance is a poor conductor.

Resistance of a conductor depends on followings factors:

(i) On Length of conductor.

(ii) On Area of cross-section of conductor. 

(iii) On the nature of conductor's materail. 

Relation among Length, Area and Resistance:

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

This gives:

          R ∝ l                              ..................  (i)

and    R ∝ l/A                           ................... (ii)

        R ∝ l/A                          using (i) and (ii) 

or, 

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

The SI unit of resistivity is Ω m.

Resistivity: Resistivity is a characteristic property of the material. S. I unit of resistivity is ohm (Ω). It is denoted by p. 

 

• The metals and alloys have very low resistivity in the range of 10^-8 Ω m to 10^-6 Ω m.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 (परिवर्तित) with temperature.

Charactristics of alloy:

(i) The resistivity of an alloy is generally higher than that of its constituent metals.

(ii) Alloys do not oxidise (burn) readily at high temperatures.

(iii) They have high melting point. 

Therefore, alloys are commonly used in electrical heating devices, like electric iron, toasters etc. Tungsten is used almost exclusively for filaments of electric bulbs, whereas copper and aluminium are generally used for electrical transmission lines.

 

Connecting resistors to a circuit: 

The current through a conductor depends upon its resistance and the potential difference across its ends.

There are two methods of joining the resistors together.

(i) Series: When two or more resistances are joined end to end so that same current flows through each of them. The resistors connecting in such manner is called resistors connected in series.

Resistors R₁, R₂ and R₃ and a bulb are connected in series

Total Equivalent Resistance in Series: 

When we connent resistors R₁, R₂ and R₃ in series, the current (I) flowing through the resistance in series will remain same in every part of the circuit, where as the potential difference (V) across each resistor will be diffrerent. 

The total potential difference across a combination of resistors inseries is equal to the sum of potential difference across the individual resistors.

Therefore,

V = V₁ + V₂ + V₃          -------------------- (i) 

When we apply Ohm's law

V = IR                           --------------------(ii) 

So for each part we get;

V₁ = I R₁     -------------- (iii) 
V₂ = I R₂     -------------- (iv) 
V₃ = I R₃     -------------- (v) 

Adding (iii) (iv) (v) 

V₁ + V₂ + V₃ = I R₁ + I R₂ + I R₃       

V = I (R₁ + R₂ + R₃ )                using equation (i) 

IR = I (R₁ + R₂ + R₃ )              using equation (ii) (V = IR )

which gives

R = R₁ + R₂ + R₃   

Here R is total equivalent resistance in series which is equal to sums of individual resistances, R1, R2, R3, and is thus greater than any individual resistance. 

(ii) Parallel: When two or more resistances are connected across two point so that each of them provides a seperate path for current, The resistors connecting in such manner is called resistors connected in parallel.

Resistors R₁, R₂ and R₃ are connected in parallel. 

Total Equivalent Resistance in parallel:

When we connect the resistors R₁, R₂ and R₃ in parallel, The current (I) following in each resistors will be difference but the potential difference (V) across the each resistors will be same. 

Therefore,

I = I₁ + I₂ + I₃        -------------- (i)  [current is difference in each resistor]

Let R_p be the equivalent resistance of the parallel combination of resistors.  

By applying Ohm’s law to the parallel combination of resistors.

On applying Ohm’s law to each resistor, we have

adding equation (iii) (iv) and (v) 

Effect on current when resistors are connected in series: 

Let, Two resistors R₁ and R₂ of 3 Ω and 5 Ω are connected in series to a 6 V battery. What will be toatal resistance of circuit and current through the circuit.

Total resistance in circuit

R =  R₁ + R₂ 

   = 3 Ω + 5 Ω​ 

   = 8 Ω 

Now calculating for Current;

I = V/R 

  = 6/8 

  = 0.75 A 

Effect on current when resistors are connected in parallel: 

Same divices connected in parallel then resulting total resistance (R) and current (I)

Now calculating for Current;

See these result in a table 

Resistor	Resistance	Current
Series	8 Ω	0.75 A
Parallel	1.875 Ω	3.2 A

Battery: Connections of two or more than two cells is callled battery. 

Ohm's Law

Ohm's Law: the electric current flowing through a metallic wire is directly proportional to the potential difference V, across its ends provided its temperature remains the same. This is called Ohm’s law.

V ∝ I

V ∝ I.constant

V/I = constant 

      = R

  V = IR 

Resistance 

 

Heating Effect of electric current:

The chemical reaction within the cell generates the potential difference between
its two terminals that sets the electrons in motion to flow the current through a resistor or a system of resistors connected to the battery.

Some of energy of the source (cell or battery) is used to maintain the current and consumed in usefulwork. Rest of the source energy may be expended in heat to raise the temperature of gadget. 

For example, an electric fan becomes warm if used continuously for longer time etc.

On the other hand, if the electric circuit is purely resistive, that is, a configuration of resistors only connected to a battery; the source energy continually gets dissipated entirely in the form of heat. This is known as the heating effect of electric current.

joule's law of heating: 

The heat produced in a resistor is directly proportional to the square of current
for a given resistance, directly proportional to resistance for a given current, and  the time for which the current flows through the resistor. This law is called the joule's law of heating. 

Joule's law heating is denoted by "H"

H = I²Rt

Establishment of this law in formulla: 

Let us suppose that current (I) is flowing through a resistor of resistance
(R) for the time (t). The potential difference across the resistance is (V).

The law stated that the heat produced in a resistor is :

(i) Directly proportional to the square of current (I) for a given resistance.

(ii) Directly proportional to resistance (R) for a given current.

(iii) Directly proportional to the time for which the current flows through the resistor.

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