Current Electricity Chapter 3 Class 12/ NEET/ JEE

 Introduction 

In electrostatics, we studied the charges at rest . In this chapter we will study the charges in motion constitute an electric current. Such currents occur naturally in many situations. Lightning is one such phenomenon in which charges flow from the clouds to the earth through the atmosphere, sometimes with disastrous( dangerous  ) results.The flow of charges in lightning is not steady,but in our everyday life we see many devices where charges flow in a steady( continuously same rate )manner ,like water flowing smoothly in a river,A torch and a cell - driven clock are examples of such devices We shall discuss the steady electric current in this chapter.

Current Carriers

The charged particles which constitute( banana ) an electric current in solids, liquids, gases are known as current Carriers.

a) Solids : In conductors ( metals like copper, silver, aluminium etc.) ,free electrons constitute an electric current.Electrons in the outermost orbits of the atoms i. e valence electrons of conductors are loosely bound. These electrons can move about in the whole conductor and are known as free electrons.Under the effect of external electric field, these free electrons move in a direction opposite to the direction of electric field and constitute electric current. Thus ,free electrons or valence electrons are the current Carriers in conductor.

In insulator, all the electrons are tightly bound to their parent atoms. Hence they do not have free electrons and as such there is practically no current carrier in an insulator.

In semi - conductors, the current carriers are free electrons and holes.

b) Liquid : The positive and negative ions are the current carriers in the liquids.

c) Gases : Positive ions and electrons are the current carriers in gases.

Electric Current 

Electric current is defined as the amount of electric charges flowing through any cross - section of a conductor per unit time. Or Electric current is defined as the rate of flow of electric charges through cross - section of a conductor.

Let charge Q crosses through a cross - section of a conductor in time t, then 

Electric current, I = Q/ t     .......(i)  

If n electrons ,each of charge e ( = 1.6 × 10 ^ -19 ) cross through a cross - section of a conductor in time t, then Q = ne , we get

I = Q/ t = ne/ t    ......(ii)

Units of Electric current : The S.I unit of electric current is ampere ( A).

1 ampere(A)  = 1 coulomb ( C) / 1 second ( s) = 1 C/ s

Definition of ampere : Electric current through a conductor is said to be one ampere, If charge of one coulomb flows through any cross - section of the conductor in one second.

Commonly used smaller units of electric current are milliampere ( 1 mA = 10^(-3)A or 1/1000 A ) and microampere ( 1 uA = 10^(-6) A).

Direction of Electric Current : The direction of flow of positive charge gives the direction of electric current. This current is known as conventional current.

It is called conventional current because in the beginning,it was thought that electric current is due to the flow of positive charges.However,in a conductor,the flow of electrons ( i.e..., negative charge) constitute electric current.The direction of flow of electrons is opposite to the direction of conventional current.

Nature of Electric Current : Electric current is a scalar quantity. Although electric current has magnitude as well as direction yet it is not a vector quantity.

For example, consider three metallic wires A, B and C meeting at a point or junction O in

 fig. Let 2 A and 3 A currents flow through the wires A and B respectively. Then the current in third wire C is 5 A ( = 2A + 3A ). Thus , steady electric current are added algebraically.

Measurement of Electric Current : Electric current is measured by an instrument called ammeter.

The ammeter is always connected in series with the circuit in which the current is to be measured. An ammeter should have very low resistance.

Types of Current 

(i) Steady Direct Current : An electric current is said to be steady ( i.e.. constant or regular ) direct current if it's magnitude and direction do not change with time. In fig. ( A) shows a graph between steady current ( I)  and time ( t).

(ii) Varying or Variable Direct Current : An electric current is said to be varying ( changing ) direct current if it's magnitude changes with time and polarity remains same. In fig.( B) the variation of variable current ( I ) with time ( t)  by  three different curves P, Q and R.

( iii ) Alternating Current : An electric current is said to be alternating current if it's magnitude changes with time and polarity ( + or - ) reverses periodically ( after regular intervals of time ). The alternations of current with time are shown in fig.( C).

Instantaneous Current : If the net charge ∆Q crosses the shaded cross - sectional area ( figure.2) in a time ∆ t,then instantaneous current across the conductor is given by

The charge that passes through the given cross - section of the conductor in a time interval from 0 to t is given by 

where,I varies with time t .

Note :1)  In case of a discharge tube, current carriers are electrons and positively charged ions, therefore, total current through a given cross - section of discharge tube, 

I = e( ne + np)/t

Where,ne = number of electrons 

np = number of protons

e = charge on electron or proton.

2) The current in human nerve is of the order of microampere ( uA ).

3) Average current during lightning is of the order of tens of thousands of ampere.

4) Passage of electric current more than 0.015 A through human body can be fatal.

Explanation : 2) Current in human nerve is of the order of microampere (µA)

Human body ke nerves me jo electrical signals travel karte hain, unme current bahut chhota hota hai.

Microampere ka matlab: 10 ^ (-6)

Yani 1 ampere ka 1000000 hissa.

Nerve cells (neurons) ions ki movement se tiny electric signals bhejte hain, isliye current bahut small hota hai.

3) Average current during lightning is of the order of tens of thousands of ampere

Bijli (lightning) me bahut huge amount of charge bahut kam time me flow karta hai.

Isliye current extremely large hota hai — around:

Yani 10,000 se 100,000 ampere tak.

Isi wajah se lightning dangerous hoti hai — heat, light aur sound bahut powerful hote hain.

4) Passage of electric current more than 0.015 A through human body can be fatal

0.015 A = 15 milliampere (mA).

Agar itna ya isse zyada current body se pass kare, to:

muscles contract ho sakte hain,

breathing affect ho sakti hai,

heart rhythm disturb ho sakta hai,

electric shock deadly ban sakta hai.

Isi liye household electricity bhi dangerous hoti hai agar proper safety na ho.

3.3 Electric Current in Conductors

NCERT Line Explanation : Jab kisi electric charge par electric field lagayi jati hai, to us par force lagta hai. Agar charge free ho move karne ke liye, to wo move karega aur current produce karega. Nature me kuch jagah free charged particles milte hain, jaise atmosphere ke upper layer ionosphere me. Lekin atoms aur molecules me negatively charged electrons aur positively charged nucleus ek dusre se bound hote hain, isliye freely move nahi kar pate.

Koi bhi bulk matter bahut saare molecules se milkar bana hota hai. Example ke liye, 1 gram water me lagbhag 10 ^ 22 molecules hote hain. Molecules itne close packed hote hain ki kuch electrons individual nuclei se tightly attached nahi rehte. Kuch materials me electrons fir bhi bound rehte hain, isliye electric field lagane par bhi accelerate nahi karte. Lekin metals jaise materials me kuch electrons almost free hote hain aur material ke andar easily move kar sakte hain. Aise materials ko conductors kehte hain. Jab in par electric field lagayi jati hai, to inme electric current develop ho jata hai.

Solid conductors me atoms tightly bound hote hain aur current mainly negatively charged electrons carry karte hain. Kuch aur conductors jaise electrolytic solutions me positive aur negative dono charges move kar sakte hain, lekin yahan hum sirf solid conductors ki baat kar rahe hain jahan fixed positive ions ke background me electrons move karte hain. Ab pehle wo case socho jab electric field present nahi hai. Tab bhi electrons thermal motion ki wajah se random motion karte rehte hain aur fixed ions se collide karte hain. Collision ke baad electron ki speed lagbhag same rehti hai, lekin uski direction completely random ho jati hai. Kisi ek direction me jyada electrons move nahi karte. Isliye average me net electric current zero hota hai.

Ab socho ki conductor par electric field apply ki gayi hai. Conductor ko cylinder shape me imagine karo. Cylinder ke dono ends par do circular discs lagaye gaye hain. Ek disc par +Q charge aur doosri par −Q charge diya gaya hai. Is arrangement ki wajah se conductor ke andar electric field create hoti hai jo positive se negative direction me hoti hai. Electrons negative charge wale hote hain, isliye wo +Q ki taraf move karte hain. Ye movement charges ko neutralise karne ki koshish karta hai. Jab tak electrons move karte hain tab tak electric current flow hota hai. Lekin thodi der baad charges neutral ho jate hain aur current band ho jata hai.

Agar conductor ke ends par continuously fresh charges supply kiye jayein, to electric field steady bani rahegi. Isse current bhi continuously flow karega, jise steady current kehte hain. Jo devices steady electric field maintain karti hain unhe cells ya batteries kehte hain.

Case 1 : When no electric field is present : In a solid conductor, free electrons move randomly ( i.e.. in zig - zag way ) with a thermal speed of the order of 10^5 to 10^6 m/s at room temperature. Thus on the average,the number of electrons travelling in any direction will be equal to the number of electrons travelling in the opposite direction.So ,the flow of net electrons ( or charge ) through the given cross - section of the conductor is zero.Hence, electric current in the conductor is zero.

Case 2 : When electric field is applied : An electric field will be created and is directed from the positive towards the negative charge. The free electrons in the conductor experiences a force F = - eE in the direction opposite to the direction of the electric field.

 Thus, free electrons in the solid conductor are accelerated in the direction opposite to the direction of the electric field ( -Q to + Q ) . 

Therefore, there is current in the conductor due to the movement of electrons from negative (-Q ) to + Q. They will thus move to neutralise the charges, therefore, a cell or a battery connected across the ends of a solid conductor provides a steady current in the conductor.

3.4  Ohm 's Law

State Ohm's law. How will you verify Ohm's law ? Give V- I characteristics.

According to Ohm's law, the current (I) flowing through a conductor is directly proportional to the potential difference (V) across the ends of the conductor provided the physical conditions ( like temperature, pressure,etc.. ) of the conductor remain unchanged.

where R is constant of proportionality and is known as electric resistance or simply resistance of the conductor.

The value of R depends upon the nature of the material, dimensions and temperature.It does not depend on the values of V and I.

Verification of Ohm's law

Ohm's law can be verified by voltmeter - ammeter method.A battery is connected to a conductor XY through a rheostat, ammeter and key.Voltmeter across the conductor XY measures potential difference across the conductor in fig.1

When key is closed, current flows through the conductor. Reading of voltmeter and ammeter are noted for different positions of rheostat. It is observed that V/ I = constant.Thus ,Ohm's law is verified.

V - I Characteristics 

The variation of V and I through two conductors A and B is shown in fig 2. It is represented by a straight line having a constant slope = V/ I = R. Higher slope of V- I curve means higher resistance,so conductor B has higher resistance than the resistance of conductor A.

Similarly, I - V graph is shown in fig.3. Slope of I - V curve is I/ V = 1/R . Thus, resistance of a conductor is inversely proportional to the slope of I - V curve.

Thus, resistance of a conductor is large whose slope of I - V curve is small. Hence, resistance of conductor B is higher than the resistance of conductor A.

Electrical Resistance 

What do you know about resistance ? Give and state SI unit of resistance. Give dimensions of resistance. What is the causes of resistance in a conductor ?

Resistance of a conductor is the opposition offered to the flow of electric charge in the conductor.

It is defined as the ratio of the potential difference across the ends of the conductor to the current flowing through it. i.e R = V/ I

Cause of Resistance of a conductor : Electrical resistance is the opposition offered by the conductor to the flow of electric charge ( i.e electrons ) . When a conductor is connected across a cell or battery,free electrons in the conductor flow from negative terminal to the positive terminal of the battery. This gives rise to the electric current in the conductor.When free electrons flow from one end to another end of the conductor, they collide with the ions in the conductor. This collision offers opposition or resistance to the flow of electrons through the conductor. The electrical resistance depends upon the nature of the material because the arrangement of ions in different material is different. The resistance also depends on the length, thickness and the temperature of the material.

• Resistance of a conductor can be measured with the help of an instrument known as ohmmeter.
• Resistance of a human body,when skin is dry is about of 10^5 ohm, However, if the skin is wet , resistance of human body is about 1500 ohm.

Electrical Resistivity or Specific Resistance 

Define resistivity or specific resistance. Mention factors on which it depends.Give S.I unit and dimensional formula of resistivity.

Resistivity is the property of a  material that opposes the flow of electric currents.

It has been found by experiments that :

a) The resistance ( R) of a conductor is directly proportional to its length (l).

                         i .e.     

b) The resistance ( R) of a conductor is inversely proportional to its area of cross - section ( A).

Resistivity of a conductor depends on the nature of the material and temperature,it doesn't depend on the dimensions ( length, area or thickness ). If temperature of a conductor increases, it's resistivity also increases. If the temperature of a conductor decreases ,it's resistivity also decreases.

Conductance and Conductivity 

Conductance of a substance is equal to the inverse of its resistance.

Conductivity of a substance is equal to the inverse of its resistivity.

3.5 Drift Velocity 

Define drift velocity. Drive and expression for drift velocity.

Drift velocity is defined as the average velocity with which free electrons in a conductor get drifted in a direction opposite to the direction of the applied electric field.

• The drift velocity is of the order of 10^(-4) m/ sec which is negligible as compared to the average electron thermal velocity of 10 ^ 6 m/ sec at room temperature.
• relaxation time and n are constants and independent of electric field.

Define mobility. State S.I unit of mobility.

Mobility of a current carrier is the ratio of the drift velocity of current carrier in a material to the applied electric field across the material.

Thus, mobility of a current carrier is inversely proportional to the mass of the current carrier. Mobility is positive,it's practical units 10^4  cm^2 / Vs.

For example,in a semiconductor, mobility of an electron is more than the mobility of a hole because electron is lighter than the hole.

Derive relation between drift velocity and electric current.

Consider a conductor of length l and uniform cross - section area A. Let V be the applied potential difference across the ends of the conductor in fig.

The magnitude of electric field is E = V/ l

Let n be the number of free electrons per unit volume of the conductor.Then,total number of free electrons in the conductor = n × volume of the conductor = n × Al.

If e is the magnitude of charge on each electron,then the total charge in the conductor, Q = ( nAl ) e    .........(i)

The time taken by the charge to cross the conductor length is given by 

t = l / vd, where vd = drift velocity of electrons.

According to the definition of electric current,

Derive Ohm 's law using first principles.

Let v_d be the drift velocity of electrons through a section of the conductor of length l and cross - sectional area A. V is the potential difference across the section of the conductor,and E is electric field.

The electric current in the conductor is ,I = neAv_d .

where n = number of electrons per unit volume in the conductor.

But magnitude of drift velocity, 

What is current density ? Derive a relation for it .

Current density of a conductor is defined as the amount of current passing per unit area of the conductor held perpendicular to the flow of charges.

i.e.                 Current Density ( J ) = Current ( I )/ Area ( A)

               

or,                      J = I / A

Current density is a vector quantity and it's direction is same as that of the direction of the conventional current ( or in the direction of flow of positive charges ).

The current ( dI ) through an element of the surface area dA of a conductor is given by,

dI = J . dA

Note : Magnitude of current density at the surface of a cylindrical conductor is zero.

Derive microscopic form of Ohm ' s law .

We know that current,       I = neAv_d , where v_d = drift velocity.

where J is the current density and p is the resistivity of the substance.

Note : Drift velocity in terms of voltage applied across the conductor.

v_d. = I/ neA = V/ neAR.  [ I = V/ R ]

But.    R = pl/ A

Then v_d = V/ nepl

Thus, drift velocity is directly proportional to the applied voltage and inversely proportional to its length.

3.6 Limitations of Ohm's Law 

Ohm’s law states: Potential difference ( V) is directly proportional to the Current ( I ) , or V = I R ......(i)

This law is valid only when temperature and physical conditions remain constant.

Although Ohm's law has been found valid over a large class of materials, there do exist materials and devices used in electric circuits where the proportionality of V and I does not hold. The deviations broadly are one or more of the following types :

Hindeng : Ohm’s law bahut saare materials ke liye sahi kaam karta hai.

 Lekin kuch materials aur devices aise hote hain jahan Voltage (V) aur Current (I) directly proportional nahi hote. 

a) V ceases to be proportional to I , or V is not directly proportional to I.

For example :  Bulb filament

• Bulb on karte waqt:
• filament thanda hota hai
• current zyada flow karta hai
  
  
  
• Thodi der baad:
• filament garam ho jata hai
• resistance badh jata hai
• current proportional nahi rehta
• Isliye graph curve ban jata hai.

b) The relation between V and I depends on the sign of V . In other words, if I is the current for a certain V , then reversing the direction of V keeping it's magnitude fixed,does not produce a current of the same magnitude as I in the opposite direction.This happens, for example, a diode.

Explanation : Diode ek direction me current ( positive direction or forward biased ) easily pass karta hai, aur opposite direction ( Negative side or reversed biased ) me almost block karta hai. Isliye V-I graph symmetric straight line nahi hota.

Condition.        Voltage.    Current 

Forward bias.  Positive.     Large ( mA )

Reverse bias.    Negative.   Tiny negative ( micro A ).

c) The relation between V and I is not unique, i.e.. there is more than one value of V for the same current I. Example : GaAs

Non-linear region : V is not directly proportional to the current. example : bulb filament 

Negative resistance region : slope is negative and voltage is increased with current is decreased. example : GaAs

Note : Every negative resistance region is non-linear, but every non-linear region is not negative resistance region.

Ohmic Devices : copper wire, metallic conductor, graph is straight line, 

Non-ohmic Devices : diode, transistor,semiconductor, graph is non - linear / curved line.

Jo devices Ohm’s law follow nahi karte,usi device ka use electronic circuits me maximum hota hai.

3.8 Temperature Dependence of Resistivity 

It has been observed that at low temperature, resistivity of a conductor increases at a higher power of temperature ( T) . Thus, over a limited range of temperature,the variation of resistivity at temperature T is expressed by the relation

Thus, temperature coefficient of resistivity is defined as the change in resistivity per unit original resistivity per unit change in temperature. It's S.I unit is K ^ (-1), where K = kelvin.

temperature coefficient of resistivity is different for different materials.

( i) Metals / Conductors : Temperature coefficient of resistivity is positive i.e.. their resistivity increases with increase in temperature. In most of the metallic conductors ( Nichrome is an alloy of nickel,iron and chromium, Manganin, Constantan ) ,the resistivity increases linearly with increase in temperature. At low temperature,the conductor like copper, aluminium etc. have non - linear dependence.

ii) Semi - conductors : Temperature coefficient of resistivity is negative. Germanium and Silicon are the semiconductors. At 0 K , semiconductors behave as insulators but at room temperature,they behave as conductors.

The resistivity of a semiconductors depends on, the temperature variation and the suitable impurities added in the semiconductor. A small amount of specific impurities added in the semiconductors decrease their resistivity to a large extent. Also with the increase in temperature,the resistivity of the semiconductors decreases more rapidly.

iii) Insulators : Resistivity of insulators ( like wood, glass ,etc. ) decreases exponentially with decrease in temperature.The resistivity of insulators at absolute zero is infinity large.

Factors Affecting Resistivity and Conductivity 

i) Dependence of Resistivity and Conductivity on number of free electrons per unit volume : The number of free electrons per unit volume ( n) is different in different materials, therefore, resistivity and conductivity depends on the nature of the material of the conductor.

ii) Dependence of Resistivity and Conductivity on Relaxation time : Relaxation time decreases with the increase in temperature. Therefore, resistivity is inversely proportional to the relaxation time or directly proportional to the temperature, hence resistivity of a conductor increases with increase in temperature otherwise conductivity of a conductor decreases with increase in temperature.

Note : For ideal conductor, resistivity is zero and for ideal insulator,the resistivity is infinite. However,for real conductors, insulators and semiconductors,the resistivity varies over a wide range. Metals have low resistivities in the range of 10 ^(-8) to 10 ^(-6), insulators having resistivities 10^18 times greater than metals or more. In between the two are the semiconductors.

Effect of Temperature on the Resistance of a Conductor 

Resistance offered by a metallic conductor is due to the collisions between drifting electrons and the ions present in the metallic conductor.

When the temperature of the conductor increases, the amplitude of vibration of ions in the lattice increases and hence the collisions between electrons and the ions become more frequent. Therefore, the opposition to the flow of electrons ( constituting the electric current) increases.In other words, resistance of the metallic conductor increases or decreases with the increase or decrease of the temperature respectively.

3.9 Electrical Energy, Power 

NCERT Explanation 

"Consider a conductor with end points A and B, in which a current I is flowing from A to B. The electric potential at A and B are denoted by V(A) and V(B) respectively. Since current is flowing from A to B, V(A) > V(B) and the potential difference across AB is V = V(A) - V(B) > 0."

Hinglish : Maan lijiye ek conductor (tar ya wire) hai jiske do ends hain, A aur B, aur isme current I, A se B ki taraf beh (flow kar) raha hai.

A point ka potential V(A) hai aur B ka V(B) hai.

Kyuki current hamesha high potential se low potential ki taraf jata hai, isliye A ka potential B se zyada hoga (V(A) > V(B)).

Dono ke beech ka potential difference (V) hoga: V = V(A) - V(B), jo ki hamesha zero se bada (positive) hoga.

Paragraph 2: Potential Energy Me Badlav (Change)

"In a time interval ∆ t , an amount of charge ∆ Q = I ∆ t travels from A to B. The potential energy of the charge at A, by definition, was Q V(A) and similarly at B, it is Q V(B)."

Hinglish : Ek chhote se time interval ∆t  me, kitna charge A se B tak gaya? Formula hota hai: ∆ Q = I / ∆ t.

Potential energy ka basic rule hai: ∆ U = Q V.

Isliye, shuruat me jab charge A par tha, to uski potential energy Q V( A), aur jab wo B par pahuncha, to uski energy Q V( B) .

"Thus, change in its potential energy ∆ U is:

= ∆ Q [ V ( B) - V ( A) ] = - ∆ Q V

= -I V ∆ t < 0" (Equation 3.28)

Hinglish : Jab hum change in potential energy (\Delta U_{\text{pot}}) nikalenge, to final energy me se initial energy ko minus karenge.

Chunki V(A) bada hai aur V(B) chhota, isliye [V(B) - V(A)] ka value negative aayega, jise hum -V likh sakte hain.

 iska matlab potential energy kam ho rahi hai (decrease ho rahi hai).

Paragraph 3: Agar Koi Collision (Takarar) Na Ho (Ideal Case)

"If charges moved without collisions through the conductor, their kinetic energy would also change so that the total energy is unchanged. Conservation of total energy would then imply that, ∆ K = -∆ U (Equation 3.29)

"that is, ∆ K = I V ∆t  > 0" (Equation 3.30)

Hinglish : Agar charges bina kisi rukawat ya collision (bina ions se takraye) ke conductor me chalte, to Law of Conservation of Energy ke mutabik total energy same rehni chahiye.

Agar potential energy kam ho rahi hai ∆U negative hai), to kinetic energy utni hi badhni chahiye  ∆K positive hona chahiye). Yani charges ki speed lagatar badhti chali jati.

Paragraph 4: Asliyat Me Kya Hota Hai? (Drift Velocity & Heat)

"Thus, in case charges were moving freely through the conductor under the action of electric field, their kinetic energy would increase as they move. We have, however, seen earlier that on the average, charge carriers do not move with acceleration but with a steady drift velocity."

Hinglish : Agar charges free chalte, to unki kinetic energy badhti aur wo accelerate hote. Lekin real life me aisa nahi hota. Humne pehle padha hai ki charges accelerate nahi hote, balki ek constant average speed se chalte hain jise drift velocity kehte hain.

"This is because of the collisions with ions and atoms during transit. During collisions, the energy gained by the charges thus is shared with the atoms. The atoms vibrate more vigorously, i.e., the conductor heats up."

Hinglish : Aisa isliye hota hai kyuki chalte waqt ye charges raste me aane wale atoms aur ions se lagatar takarate (collide karte) hain. Takrane se jo energy charges ko electric field se milti hai, wo un atoms ko transfer ho jati hai. Is wajah se wo atoms tezi se vibrate karne lagte hain, aur natija ye hota hai ki conductor garam (heat) ho jata hai.

"Thus, in an actual conductor, an amount of energy dissipated as heat in the conductor during the time interval ∆ t is, ∆ W = I V ∆t (Equation 3.31)

Hinglish : Isliye, ek real conductor me jitna work ya energy heat ke roop me barbad (dissipate) hoti hai, wo hai: \Delta W = I V ∆t.

Paragraph 5: Power Dissipated (Shakti Ka Nuksan)

"The energy dissipated per unit time is the power dissipated P = \Delta W / \Delta t and we have, P = I V" (Equation 3.32)

Define electric energy and power. Give their S.I unit and define them. Give relation between them.

Electric Energy : The work done by a source to maintain a current in an electrical circuit is known as electric energy.

Consider an electric circuit element ( e.g. an electric lamp, heater etc. ) through which current I flows from the end A to the end B for time t. Let q be the charge flowing from A to B in time t.

then   Q = It

If V be the potential difference between A and B, then work done to carry the charge Q from point A to B is given by W = Vq = VIt  ......(i)

This work done is equal to the electric energy E consumed in the circuit is given by 

 E = VIt.  .....(ii)

From Ohm's law,

V = IR ,then equ (ii) becomes 

E = ( IR ) It = I ^2 R t ......(iii)

This is the form of energy which is converted into heat energy.

Electric Power : It is defined as the rate of doing electrical work.

Or, Electric power (P) is defined as the heat energy produced per unit time in an electric device of resistance R,when current I is passing through it.

i.e.  Electric power, P = energy produced/ time 

Or, P = E/ t

Since heat energy produced in an electric device of resistance R due to the flow of electric current I is given by 

Thus, electric power is simply defined as the product of the applied voltage and current flowing through the circuit.

S.I . Units of Electric power is watt ( W ).

We know, P = VI , If P = 1 watt, V = 1 volt and I = 1 ampere 

Then, 1 watt = 1 volt × 1 ampere 

Or, 1 W = 1 ampere volt

Definition of watt : 1 watt is defined as the 1 ampere current flows through an electrical circuit, when a potential difference of 1 volt is applied across it.

Bigger unit of electric power is kilowatt ( kW ) and still bigger unit is megawatt ( MW).

1 kW = 10^3 W and 1 MW = 10^6 W

Practical unit of power is horse - power ( h.p).

1 h.p = 746 W

Note : P = VI applies to rate of electric energy transfer from a source ( say a cell or battery).

P = I^2R = V^2/R applies to the rate of transfer of electric energy to thermal or heat energy in a resistor of resistance R.

Relation between electric energy and electric power 

Electric energy, E = VIt.   ......(i)

and Electric power, P = VI.      ........(ii)

where V = potential difference , I = electric current,t = time

From (i) and ( ii )

E = Pt

Or, P = E/ t

Or, Power = Energy/ Time 

Commercial Unit or Board of Trade ( BOT) Unit of electric energy is kilowatt hours ( kWh) simply known as unit i.e .  1 unit = 1 kWh = 1000 Wh

Note : 1 kWh = 1000 watt h = 1000 J/ s × 3600 s [ 1W = 1 J/s ]

                                                  = 3600, 000 J = 3.6 × 10^6 J

Hence, 1 kWh = 3.6 × 10^6 J

Resistor, Combination of Resistors - Series and Parallel 

Resistor : Resistor is a component of an electrical circuit offering certain opposition to the flow of current in that circuit.Some resistors are made from wire wound and some are made from carbon. Both can be of two types a) Fixed ( non variable resistance ) and b) variable or rheostat ( whose resistance can be changed ).

Equivalent resistor : A single resistor which draws the same current as the given combination of resistors when the same potential difference is applied across its end points is called equivalent resistor or effective resistor or net resistor or total resistor.

(i) Series Combination : Two or more resistors are said to be connected in series of they are connected one after the other such that the same current flows through all the resistors when some potential difference is applied across the combination.

(ii) Parallel Combination : Two or more resistors are said to be connected in parallel if one end of a resistor is connected to one end of the other resistor and the second end of the first resistor is connected to second end of the other resistor such that the potential difference across each resistor is equal to the applied potential difference across the combination but currents of each resistance are different.

Cells, Battery, EMF, Internal resistance 

Cell : A cell is a device that converts chemical energy into electrical energy.

It produces a small amount of electric current. It is a device to maintain a steady current in an electric circuit is the electrolytic cell.

A cell consists of two rods called electrode which are dipped in a chemical solution called electrolyte. 

Battery : A battery is a combination of two or more cells connected together to produce more electrical energy. 

EMF ( Electromotive force ) : It is the potential difference between the positive and negative electrodes in an open circuit ,i.e. when no current is flowing through the cell.

Electromotive force is not a force but work done per unit charge. S.I unit of E.M.F is joule per coulomb or volt ( V).

E.M.F of a cell is independent of the :

• size of the electrodes of the cell.
• distance between the electrodes of the cell.
• quantity of the electrolyte in a cell.

Terminal Potential Difference : It is defined as the potential difference between its terminals in a closed circuit ( i.e. when current is drawn from the cell ).

S.I unit of terminal potential difference is Volt ( V ).

Internal Resistance : It is defined as the opposition offered by the electrolyte and electrodes of a cell to the flow of current through it. It is denoted by r and mainly depends on the nature of electrolytes and electrodes of a cell. S.I unit of internal resistance is ohm.

Give relation between e.m.f and terminal potential difference and thus find the expression for internal resistance.

Consider a cell of e.m.f . E and internal resistance r connected to an external resistance R through a key ( K) as shown in fig. below.

When key ( K ) is open : No current is drawn from the cell. So the voltmeter connected across the cell gives the value of e.m.f ( E). or, E = V 

When key ( K) is closed : Current, I = E/ R + r ( R and r are in series )

or,       E = IR + Ir      .......(i)

Now, V = IR ( from Ohm's law ).  ......(ii)

Hence, equal ( i) becomes 

E = V + Ir

or,V = E - Ir.    ..........(iii)

This shows that the terminal potential difference of the cell is less than the e.m.f of the cell. Now the voltmeter connected across the cell will read V < E

                      

Thus, knowing the values of E, V and R, we can determine the value of R.

What is Carbon resistor ? How to read the value of a resistor ?

A carbon resistor is a fixed resistor made mainly from carbon material with a suitable binding material is moulded into a cylinder. It is used in electronic circuits to limit current and control voltage.

Types of carbon resistors

Carbon composition resistor – made from carbon powder and binder.

Carbon film resistor – made by depositing a thin carbon layer on a ceramic rod.

They are commonly used in radios, TVs, amplifiers, and electronic circuits.

How to read the value of a resistor ?

The values of the resistances of the carbon resistors are indicated by three or four colour bands painted on the bodies of the carbon resistor.

These coloured bands can be translated into a number by using the standard colour code given below :

Easy memory trick

“BB ROY of Great Britain had a Very Good Wife wearing Gold Silver Necklace.

• Black
• Brown
• Red
• Orange
• Yellow
• Green
• Blue
• Violet
• Grey
• White

Example : Suppose the colour band sequence of a resistor is ( B_1) green, ( B_2) brown,( B_3) yellow and ( B-4) gold. What is the effective resistance of the resistor as per colour code ?

Solution : Here colour code sequence is green - Brown - Yellow - Gold.

Now, green = 5, brown = 1 , yellow = 10^4 and gold = 5%.

What is thermistor ? Discuss it's types and applications.

A thermistor is a highly temperature dependent resistor usually made up of the oxides of various metals like copper, iron, nickel,cobalt and also of semiconductor materials.

Temperature coefficient of resistivity of a thermistor is very high and resistance of a thermistor changes very rapidly with change in temperature.