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 10^{4} 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/m^{2} 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 10^{28}electrons / cm^{3}.
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
v_{1 }= +u_{1 }a_{1}, u_{1}– initial velocity, τ_{1}– 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
nelectron 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^{1}s^{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^{1}m^{1}, or mho m^{1}, or S m^{1}
Ohmic conductor
 A conductor which obeys ohm’s law.
 Eg: metals
VI graph of an ohmic conductor
Non ohmic conductors
 Conductor which does not obey ohm’s law.
 Eg : diode, transistors, electrolytes etc.
VI 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 10^{4} Ωm
 Insulators
Resistivity > 10^{4} 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 
10^{0} 
Brown 
1 
10^{1} 

Red 
2 
10^{2} 

Orange 
3 
10^{3} 

Yellow 
4 
10^{4} 

Green 
5 
10^{5} 

Blue 
6 
10^{6} 

Violet 
7 
10^{7} 

Grey 
8 
10^{8} 

White 
9 
10^{9} 

Gold 
101 
±5% 

Silver 
102 
±10% 

No color 
±20% 
4 – Band code
Example
Resistance = ( 22 × 10^{2 }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 5band 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, ρ_{0 }– resistivity at a lower temperature T_{0}, α temperature coefficient of resistivity.
 Thus for conductors resistivity increases with temperature.
Temperature coefficient of resistivity (α)
 Unit of α is ^{0}C^{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 V_{1}, V_{2 }and V_{3} are the potential drop across resistors R_{1}, R_{2} and R_{3 }respectively.
 If all the resistors are replaced with a single effective resistance R_{S} , we get
V = IR_{S}
 Thus IR_{S }= IR_{1 }+ IR_{2 }+ IR_{3}
 Therefore, the effective resistance is
R_{S }= + +R_{1 }R_{2 }R_{3}
 For n resistors
R_{S }= + + +R_{1 }R_{2 }R_{3 }……….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 = + +I_{1 }I_{2 }I_{3}
 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 (ε_{2} → ε_{2})
 For n cells in parallel
Joule’s law of heating
 The heat energy dissipated in a current flowing conductor is given by
H = I Rt^{2 }
 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) = 10^{6}W
 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 10^{6} 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 (100l).
 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
 l_{1}– balancing length with cell E_{1}
 l_{2}– balancing length with cell E_{2}
 To get the balancing length E_{1}>E_{2}
To find internal resistance Circuit diagram
 Where l_{1}– balancing length, key K_{1}open, l_{2}– balancing length, key K_{1} 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.