Class 12 Physics CHAPTER 3 CURRENT ELECTRICITY

NCERT Notes For Class 12 Physics CHAPTER 3 CURRENT ELECTRICITY Electric current, (Physics) exam are Students are taught thru NCERT books in some of state board and CBSE Schools.  As the chapter involves an end, there is an exercise provided to assist students prepare for evaluation.  Students need to clear up those exercises very well because the questions with inside the very last asked from those. 

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NCERT Notes For Class 12 Physics CHAPTER 3 CURRENT ELECTRICITY

Class 12 Physics CHAPTER 3 CURRENT ELECTRICITY

 

CURRENT ELECTRICITY

• It is the rate of flow of electric charge.
• The instantaneous current is given by

• Steady current is given by

• Electric current is a scalar quantity.
• SI unit – ampere (A)
• 1A= 1C/s
• Other units are mA= 10^-3 A, μA =10^-6 A
• Lightning is an example of transient current.
• Current in a domestic appliance is of the order of 1A.
• Current carried by lightning is of the order of 10⁴ A.
• Current in our nerves is of the order of 1 μA.
• By convention direction of motion of positive charges (direction opposite to the motion of electrons) is taken as the direction of current.

Current density (J)

•  Current flowing through a unit area held normal to the direction of current.

• Current density is given by

•  Where A –area of cross section, θ – angle between direction current and area.
• If the area is normal to the current flow, θ=0, thus
• Unit – A/m² and dimensions are [AL^-2]
• Current density is a vector quantity.

                                     → →

• Also I = JAcosθ= J A.

Mechanism of current flow in conductors

• Metals have large number of free electrons nearly 10²⁸electrons / cm³.

In the absence of an electric field electrons are in random motion due to thermal energy.

• The average thermal velocity of electrons is zero.
• In the presence of an external electric field, electrons are accelerated and acquire an average velocity.
• During the random motion, electrons collide with each other or with positive metal ions.

Drift velocity

• Average velocity acquired by an electron in the presence of an electric field.

Relaxation time

• Average time interval between two successive collisions.

Path of an electron

Relation connecting drift velocity and relaxation Time

• The force experienced by the electron in an electric field is

F =−eE , where E – electric field

• From Newton’s second law F ma= , a- acceleration, m- mass
• Thus, ma=−eE
• Therefore acceleration of electron is

• If an electron accelerates, the velocity attained is given by

v₁ = +u₁ a₁, u₁– initial velocity, τ₁– time

• Thus the average velocity (drift velocity) is given by

• Therefore the drift velocity is given by

• Where , τ – relaxation time

Relation connecting drift velocity and current

• The number of electrons in the length l of the conductor = nAl
• Where n- electron density (number of electrons per unit volume) , A – area of cross section.
• Thus total charge q = nAle, e – charge of electron
• The electron which enter the conductor at the right end will pass through the conductor at left end in time v- drift velocity of electrons v

• That is

I =nAve

n-electron density, A –area, v- drift velocity, e- electron charge

Mobility (μ)

• Ratio of magnitude of drift velocity to the electric field.

• SI unit of mobility is CmN^-1s^-1

Difference between emf and potential difference

emf	Potential Difference
The difference in potential between the terminals of a cell, when no current is drawn from it.	The difference in potential between the terminals of a cell or between any two points in a circuit when current is drawn from the cell.
Exists only between the terminals of the cell.	Exists throughout the circuit.
It is the cause	It is the after effect.
Always greater than potential difference	Always less than emf

Ohm’s law

• At constant temperature the current flowing through a conductor is directly proportional to potential difference between the ends of the conductor.

• Thus V = IR,

V- potential difference, I – current, R- resistance

Resistance

• Ability of conductor to oppose electric current.

• SI unit – ohm (Ω)

Factors affecting resistance of a conductor

• Nature of material
• Proportional to length of the conductor
• Inversely proportional to area of cross section.
• Proportional to temperature

Relation connecting resistance and resistivity

Where ρ- resistivity, A – area, l- length

Resistivity (specific resistance)

• Resistivity of the material of a conductor is defined as the resistance of the conductor having unit length and unit area of cross section.

• Unit – ohm meter (Ωm)
• Resistivity of conductor depends on nature of material and Temperature

Conductance (G)

• Reciprocal of resistance

• Unit- Ω^-1, or mho or siemens (S)

Conductivity (σ)

• Reciprocal of resistivity

• Unit- Ω^-1m^-1, or mho m^-1, or S m^-1

Ohmic conductor

• A conductor which obeys ohm’s law.
• Eg:- metals

V-I graph of an ohmic conductor

Non ohmic conductors

• Conductor which does not obey ohm’s law.
• Eg :- diode, transistors, electrolytes etc.

V-I graph of a non- ohmic conductor (Diode)

Circuit diagram for the experimental study of ohm’s law

Limitations of ohm’s law

• The relation between V and I depends on the sign of V.

It is not a universal law.

• The relation between V and I is not linear.

• The relation between V and I is not unique, i.e., there is more than one value of V for the same current I ( A material exhibiting such behaviour is GaAs)

Vector form of ohm’s law

Classification of materials in terms of resistivity

• Conductors

Resistivity between 10^-8 Ωm and 10^-6 Ωm

• Semiconductors

Resistivity between 10^-6 Ωm and 10⁴ Ωm

• Insulators

Resistivity > 10⁴ Ωm

Relation connecting resistivity and relaxation time

Copper is used as for making connecting wires

• Copper has low resistivity.

Nichrome is used as heating element of electrical devices

• Nichrome has High resistivity

• High melting point.

Why materials like constantan and manganin are used to make standard resistances?

• Resistance does not change with temperature.
• Material has high resistivity.

Resistors

The resistor is a passive electrical component to create resistance in the flow of electric current.

Symbol Constant resisstance Variable resistance

Commercial resistors Wire bound resistors

• Made by winding the wires of an alloy, like, manganin , constantan, nichrome or similar ones, around a ceramic, plastic, or fiberglass core.
• They are relatively insensitive to temperature.
• Large length is required to make high resistance.

Carbon resistors

• Made from a mixture of carbon black, clay and resin binder.
• Are enclosed in a ceramic or plastic jacket.
• Carbon resistors are small in size , and inexpensive.

Colour code of resistors

Colour	Digit	Multiplier	Tolerance
Black	0	100

Brown	1	101
Red	2	102
Orange	3	103
Yellow	4	104
Green	5	105
Blue	6	106
Violet	7	107
Grey	8	108
White	9	109
Gold		10-1	±5%
Silver		10-2	±10%
No color			±20%

4 – Band code

Example

Resistance = ( 22 × 10² Ω) ± 10%

Resistance = ( 47 × 10 Ω) ± 5%

5 – Band code

• The colors brown, red, green, blue, and violet are used as tolerance codes on 5band resistors only.
• All 5-band resistors use a colored tolerance band.

Temperature dependence of resistivity

• When temperature is increased, average speed of the electrons increases and hence number of collision increases.
• Thus the average time of collisions τ, decreases with temperature.

Metals (Conductors)

• In a metal number of free electrons per unit volume does not depend on temperature.
• When temperature is increased, relaxation time decreases and hence resistivity increases.
• The temperature dependence of resistivity of a metallic conductor is given by

• Where ρ_T – resistivity at a temperature T, ρ₀ – resistivity at a lower temperature T₀, α -temperature coefficient of resistivity.
• Thus for conductors resistivity increases with temperature.

Temperature coefficient of resistivity (α)

• Unit of α is ⁰C^-1.
• For metals α is positive.

Temperature – resistivity graph (copper)

Alloys

• Resistivity of alloys like, Nichrome, Manganin, Constantan , is almost independent of temperature.
• Thus alloys are used to make wire bound resistors.

Temperature – resistivity graph (Nichrome)

Semiconductors

• The electron density (n) increases with temperature.
• Thus resistivity decreases with temperature.
• α is negative.

Temperature – resistivity graph

Insulators

• The electron density (n) increases with temperature.
• Resistivity decreases with temperature.

Combination of resistors Resistors in Series

• In series connection same current pass through all resistors.
• The potential drop is different for each resistor.
• The applied potential is given by

V = + +V1 V2 V3

• Where V₁, V₂ and V₃ are the potential drop across resistors R₁, R₂ and R₃ respectively.
• If all the resistors are replaced with a single effective resistance R_S , we get

V = IR_S

• Thus IR_S = IR₁ + IR₂ + IR₃
• Therefore, the effective resistance is

R_S = + +R₁ R₂ R₃

• For n resistors

R_S = + + +R₁ R₂ R₃ ……….R_n

• Thus effective resistance increases in series combination.

Resistors in parallel

• In parallel connection current is different through each resistors.
• The potential drop is same for all resistors.
• The total current

I = + +I₁ I₂ I₃

• If all resistors are replaced with an effective resistor of resistance R_P, we get

• Thus effective resistance decreases in parallel combination.

Internal resistance of a cell (r)

• Resistance offered by the electrolytes and electrodes of a cell.

Factors affecting internal resistance

• Nature of electrolytes
• Directly proportional to the distance between electrodes
• Directly proportional to the concentration of electrolytes.
• Inversely proportional to the area of the electrodes.
• Inversely proportional to the temperature of electrolyte.

Relation connecting emf and internal resistance

• Effective resistance = R+r

Combination of cells Cells in series

• In series connection current is same; the potential difference across the cells is different.
• The potential difference across the first cell is

• Similarly

• Thus total potential across AC is

V_AC =V_AB +V_BC

• That is

Cells in parallel

• In parallel connection current is different and potential is same.

• Comparing this with the equation

• Or

• If the negative terminal of the second is connected to positive terminal of the first, the equations are valid with (ε₂ → -ε₂)
• For n cells in parallel

Joule’s law of heating

• The heat energy dissipated in a current flowing conductor is given by

H = I Rt²

• I- current, R –resistance, t –time

Electric power

• It is the energy dissipated per unit time.

• SI unit is watt (W)
• 1 kilo watt (1kW) = 1000W
• 1mega watt (MW) = 10⁶W
• Another unit horse power (hp)
• 1 hp = 746 W

Electrical energy

• Electrical energy = electrical power X time
• SI unit – joule (J)
• Commercial unit – kilowatt hour (kWh)
• 1kWh = 3.6 x 10⁶ J.

Efficiency

• The efficiency of an electrical device is

𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟

𝜂 =

𝑖𝑛𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟

Kirchhoff’s rule

First rule (junction rule or current rule)

• Algebraic sum of the current meeting at junction is zero.
• Thus , Current entering a junction = current leaving the junction

Sign convention

• Current entering the junction – positive
• Current leaving the junction – negative

Second rule (loop rule or voltage rule)

• Algebraic sum of the products of the current and resistance in a closed circuit is equal to the net emf in it.
• This rule is a statement of law of conservation of energy.

Sign convention

• Current in the direction of loop – positive
• Current opposite to loop – negative

Illustration

Wheatstone’ s bridge

Wheatstone’ s principle

Derivation of balancing condition

• This is the balancing condition of a Wheatstone bridge.

Meter bridge (slide wire bridge)

• Works on Wheatstone’s principle.

• Used to find resistance of a wire.

Circuit diagram

• Where k – key, X – unknown resistance, R- known resistance, HR- high resistance, G – Galvanometer, J – Jockey

Equation to find unknown resistance

• From wheatstone’s principle

• Here P – unknown resistance , Q- known resistance, R- resistance of the wire of length l , S – resistance of wire of length (100-l).

• The length l for which galvanometer shows zero deflection – balancing length.
• Thus

• Where r – resistance per unit length of the meterbridge wire.
• Therefore the unknown resistance is given by

• The resistivity of the resistance wire can be calculated using the formula

Where r – radius of the wire, l –length of the wire.

Potentiometer

• A device used to measure an unknown emf or potential difference accurately.

Principle

• When a steady current (I) flows through a wire of uniform area of cross section, the potential difference between any two

points of the wire is directly proportional to the length of the wire between the two points.

Uses of potentiometer

• To compare the emf of two cells
• To find the internal resistance of a cell

Comparison of emfs Circuit diagram

• l₁– balancing length with cell E₁
• l₂– balancing length with cell E₂
• To get the balancing length E₁>E₂

To find internal resistance Circuit diagram

• Where l₁– balancing length, key K₁open, l₂– balancing length, key K₁ closed.

Why potentiometer is preferred over voltmeter for measuring emf of a cell?

• In potentiometer null method is used, so no energy loss in measurement.