Current

Rate of flow of charge through any cross section of wire

Dimension Q= AT

SI unit 1Ampere (A)= If 1Columb of charge flow though unit cross section in 1 sec

Its is Tensor or Scalar quantity:- Doesn’t follow to vector law of addition

Direction I- According to Convention is from +ve Terminal to –ve of battery
& e- move in opposite direction

Charge Carrier 1) Metal – free e- 2) Electrolyte- Ion 3) Gases -Free e- & Ion
Copper Free e- density- n= 1023 free e- /m3

Current Density (J)

Current flowing per unit area of cross-section held perpendicular to flow of charge.
Its vector quantity & direction same as current.

SI unit Ampere/meter2 , Dimension= AL-2

Drift velocity (Vd) (Order of Vd is 10-4 m/s, Order of Thermal velocity 105 m/s,)
The Average velocity with which free electrons are drifted to the +ve end, When p.d applied
across the end of conductor

Derivation
In the absence of Electric filed, the e- inside the conductor with a initial velocity u due to
thermal energy (speed 105 m/s)

---(1) (Due to random motion of e- ,Initial avg velocity is zero)

If ' V ' is p.d applied across the end of conductor of length ' L
Then Electric field E= V/L ------(2)
Each Electron (e- ) experience a force F=−eE - (3)
-ve sign shows direction of force opp. to electric field.

If m is the mas of e- then according the newton law F=ma ---(4)

From equ 3 & 4 ma= eE ----(5) It’s a constant acceleration

Because of continuous collision inside the conductor e- move with constant, small velocity in
the direction opposite to net electric field – Drift velocity (10-4 m/s)
The Average Velocity
Final velocities(v) of each e-
v 1 = u 1 + a τ1
v 2 = u 2 + a τ2
--
= 0 + a τavg put equ --1 --
Vn = u n + a τ n
= put equ – 2 τ–Relaxation time bet 2
successive collision
Drift velocity =
λ Free Path betn 2 collision

Note

If P.d constant Vd α 1/L (e.g Conductor in Parallel )

If Length constant Vd α V

Relationship between electric current intensity & Vd or Prove I = VdenA

Let a conductor having area of cross section A, length L, on applying potential V, current I flow.
Let Number of free electron per unit volume = n ( Free e- density = 1029 e- /m3 )
Volume= AL
Total number of free e- = e- density x Volume = = N = nAL
Total Charge Q = Ne = neAL

drift velocity

Note – , If Current is constant Vd α 1/A (Conductor connected in series)

Mobility of electron- Drift velocity per unit electric field

Graph between µ & E

 If Constant potential applied across the metallic conductor of non-
uniform cross section only Current remain constant.
Current density, electric field, & drift speed are all inversely
proportional to cross-sectional area.

Electric Potential at a point, Work done to move a unit charge from infinity to a point

Potential deference (V) – Work done to move a unit charge from 1 point to another.
( 1J of work done to move 1C of charge)
Dimension – w/q= F.S/q= m.a. S/q = M. LT-2 L / AT = ML2T-3A-1

Ohms law
The Current flowing through a conductor is directly proportional to Potential difference (v)
applied across its end, Provided all Physical conditions & temperatures remain constant
V α I , V=IR (R- constant Resistance)
Ohmic Circuit - Obeys ohms law Non-Ohmic Circuit- Do not obey ohms law

Limitation of ohm law

1) Non ohmic circuit
2) If large current flow, According to H= I2 RT heating takes place & Resistance of conductor
increses, Because of high R, I decreses & we get curve line instead of st line at high temp

Resistance – The property of conductor to resists the flow of current though it.
R is 1ohm --if we apply a P.d of 1V & 1A of current pass through a
conductor.
Dimension V/I= w/q.I= F.S/q.I= m.a.s/q.I= M.LT-2 L / AT.A = ML2T-3A-2

Cause of resistance –Collision of e- inside the conductor

Resistance of conductor Proportional to ρ is constant

Specific Resistance or Resistivity (ρ) = , SI unit is ohm meter, Ωm
Resistance offered by conductor having unit length & unit area of cross section (unit Volume)
It depends upon nature of material & temperature, does not depends on length & area

Exam plot a graph

Resistivity increases with temperature α –temperature coefficient of resistivity

α +ve for metal , -ve for semiconductors & insulators

Resistance Resistivity
It depends on L & A of conductor It does not depends on L & A
SI unit ohm SI unit ohm/meter
Resist flow of I by a conductor Resist flow of I by a unit L & unit cross section A of conductor

Volume constant:- A conductor of length stretched thrice its length, or compressed to ½

New Resistance n= 3 if stretched or (1/2) Compressed
New Voltage to keep current same is

New L=3L, A= (1/3)A, New resistance = 9R (if bubble gum stretched it becomes thin)

Conductance (G)Reciprocal of resistance G=1/R, SI unit= ohm- or mho or Siemen(S)

Conductivity (σ) is reciprocal of resistivity σ = 1/ρ =L/RA

Resistance in series (V different, I same)
If there is one to proceed from one resistance to another
V = V1+V2+V3 (V=IR)
IR =IR1+IR2+IR3 R=R1+R2+R3
Note – If Identical resistance
Rs is always greater than individual resistance

Resistance in Parallel (V Same, I different)

If there are more than one to proceed from one resistance to another
I = I1+I2+I3 V/R =V/R1+V/R2V/R3

Note – If Identical resistance

Total resistance is always less than individual resistance
Deduction of ohm law or to prove
Consider a conductor of length L, cross-sectional area A. When a p.d V is applied across its ends,
the current produced is I. If n is the number of electrons per unit volume in the conductor & Vd
the drift velocity electrons, then the relation between I & Vd is
I = VdenA ----- (1) According to ohms law
All values are constant if ---(4)
------(2) temp is constant -----(3)
This implies V α I
Put 2 in 1 From equ 3 &4

Drive a relation between, resistivity, mass, e- density, relaxation time To prove

---- (1) ---(2) Comparing 1 & 2

Types of material
1) Conductor Materials which allow current to pass through them. -- Conductivity is very high
e.g Cu, Ag,
2) Insulator Materials which do not allow current to pass through them. Conductivity is very
low or Nil e.g wood, rubber
3) Semiconductor- Materials which partially conducts electricity, ie they do not conduct at low
temp, but as temp increases they start conducting. Conductivity lies betn conductor & insulator
e.g Germanium, Silicon

Effect temp on Resistance With increase in temp kinetic energy of free e- raises & relaxation
time decreases
ΔR α Ro Δt R- final
ΔR = α Ro Δt resistance
R – Ro = α Ro(t–to)
Change in resistance depends on α = temp coefficient to –Initial
R = Ro + α Ro(t–to)
1) Initial resistance Ro, ΔR α Ro temp
R = Ro [1+ α(t–to)]
2) Rise in temp Δt, ΔR α Δt

Temp coefficient(α) Relative resistance per degree change in temp in celecius

1) For Conductors:- α is +ve, therefore Resistance increases with raise in temp

2) Effect on Insulators & Semiconductors α is -ve, Resistance decreases with raise in temp
3) Thermistor-Materials which are heat sensitive, Their resistances changes rapidly which
change in temp
Nichrome wire used in heaters is an e.g
4) Superconductors- Materials which have zero or negligible resistance.
There is no material is Superconductor, but Hg at low temp tends of behave as Superconductor
 Vector form of ohm’s law, J= σ E
J=I/A
Relation between, J, σ , E { , }
I = VdenA ---(1) ----(2)
=
Put 2 in 1
Color coding of Carbon Resistor
Resistor is a passive electrical component with 2 terminals that are used for either limiting or
regulating the flow of electric current in electrical circuits.
Commercially 2 types of resistors
1) Alloys (wire wound)- Nichrome, Manganin, Constantan
Resistivity nearly independent of temperature
Limitation – Very high resistance cannot be obtained practically - Huge in size & expensive
2) Carbon Resistor – Consists of Ceramic core on which a thin layer of crystalline Carbon is
deposited.
They can provide very high resistance,
Small in size- cannot write/or see their resistance, we use color coding to know their resistance.
4 Co-axial Bands (Rings)
Colour- 1,2/Number 3/Multiplier (10th ) 4/Tolerance or error
1, 2 & 3rd Power value 4th band
0 B Black Gold + 5%,
1 B Brown Silver +10%,
2 R Red No color +20
3 O Orange Or
4 Y Yellow Gold 10-1
5 G Green Silver 10-2
3rd digit 1st Green-5
6 B Blue 2nd –Blue-6
Multiplier
7 V Violet value 3rd – orange 103
8 G Grey 4th –Gold + 5%
9 W White Ans- 56 x 103 Ω + 5%
BB ROY Great Britain Very Good Wife, Gold Silver No color
Types of current
Alternating Current Direct Current
Current whose Magnitude Whose magnitude & direction
changes continuously but remain same eg. Battery
direction changes
Periodically E.g- home
EMF-Electromotive force (the force with which electron is moved)
P.d across the terminal of cell when it is not in use (open circuit). The potential is emf

TPD- Terminal potential difference

Potential across the terminal of cell when it is in use (closed circuit) EMF if always > TPD

Cell It is device convert chemical energy to electrical energy , Battery- more than 1cell

Internal resistance Resistance offered by cell when it is in use. Represented by ‘r”

It is always added to external resistance
Cell connection Opposite terminal E1+E2 Same terminal E1-E2 (if E1>E2)

Factors affecting internal resistance

1) Nature of electrodes 2) Nature of electrolyte (conc of electrolyte)
3) Gap between electrodes 4) Area of electrodes

To prove E= V +Ir or Relation between TPD & EMF

Let cell having emf of E connected to resistance R, Current I start flowing in the circuit
Let r is internal resistance
Maximum current flows when Note
1) Emf > TPd(V) (when cell is
 I(R+r) = E  IR +Ir = E giving I)
2) While charging Cell or battery
E= V + Ir (V=IR) V= E-Ir
Tpd > Emf E= V – Ir 1mark
3) Cell connected in open circuit
I=0, Ir=0, E=V

Expression for Internal resistance or To Prove

According to relation of emf & Tpd

E= V + Ir  Ir = E-V,   (I=V/R)

Note- At maximum power dissipation is if r= R, Tpd become ½ of emf

, , ,

Grouping of cell 3 ways 1) Series 2) Parallel 3) Mixed

1) Series grouping of cells
Let n number of cells each having emf E & internal resistance r are connected in series with
external resistance R
Net current

(I = V/R)
Since n number of cell are connected in series
Net emf in circuit Ĕ= E+E+-----En = nE, For maximum current in
Net internal resistance ř= r+r+----rn =nr circuit, the value of internal
resistance(r) must be very
small compared to external R
Sp. Case 1) r << R (r=0) 2) r >> R (R=0) (In case 1 E is getting multiplied
by n, hence max I)

2) Parallel grouping of cells

Let n number of cells each having emf E & internal resistance r are connected in parallel with
external resistance R
Net current

(I = V/R)
Since n number of cell are connected in Parallel,
Net emf in circuit Ĕ= E (As n No cell in parallel voltage remains same)
Net internal resistance 1/ř= 1/r+1/r+----1/rn = 1/nr. ř = r/n For maximum
current in circuit, the
, , value of internal
resistance(r) must be
Sp. Case 1) r << R (r=0) 2) r >> R (R=0) very Large compared
to external R
Mixed grouping of cell
Let n number of cells each having emf E & internal resistance r are connected in Series , m
number of such rows are connected in parallel with external resistance R

Net current --- (1)

As n number of cell connected in series, net emf is nE & net internal
resistance nr in 1 row
In Parallel Net emf =nE ( as potential same) ---(2)
Internal resistance-

, ----(3)

, Put 2 & 3 in 1
Condition for maximum current if nr +mR is minimum or nr=mR
Krichhoff’s Law - 2 laws
1) Krichhoff’s 1st, Current or junction law (KCL) Based on Conservation of Charge
Algebraic sum of all the current entering or leaving the junction is equal to zero, ΣI = 0
At any junction, Sum of Current entering jn = Sum of current leaving jn

If i = -ve, our assumption of direction is opposite to actual direction

1) Krichhoff’s 2nd , Voltage or Mesh or Loop law (KVL) Based on Conservation of Energy
Algebraic sum of change in potential around a closed loop is zero,
ʃ +V1 +V2 +V3 + ------+Vn =0 ΣΔV= 0 ΣE + ΣIR = 0
Potential gain = +V, Potential drop = -V

+E –IR1–IR2–IR3 =0

How to apply Krichhoff’s law

1) Draw current from one or more cells, Follow KCL law for distribution of current.

2) Choosing the loop/loops

Should be closed & can involve any No of cells, resisters, Capacitors etc
3) Direction of loop-Path – Clock wise or Anti-clock wise
4) Potential drop or Potential gain, higher to lower ΔV= -Ve, wise versa
Cell-

Cell- Path +ve(H) to –ve(L) ΔV= -Ve (No relation to current)

Resistance- Path & I in same direction IR= -Ve
Try to take current direction from higher Potential battery

Point potential method

https://www.youtube.com/watch?v=rPim2VZJ7l0

notes
https://www.studypur.com/2023/03/current-electricity-notes-class-12-free.html
https://www.studypur.com/p/physics-handwritten-notes-class-12.html

Meter Bridge
It is electrical instrument used to measure unknown resistance
It work on the principle of the Balanced Wheatstone bridge. It is based on null
deflection wherein there is no current flow in the middle of the circuit when the resistance
ratios in the arms are equal.

low-temperature coefficient of resistivity alloys like maganin, constantan, or nichrome are

used, temp has less effect on them
Lichoft volt law
https://www.youtube.com/watch?v=CuAaCROB-DM

EMF QUESTION
https://www.youtube.com/watch?v=rNbfCxJhRy4
CEELS
https://www.youtube.com/watch?v=29oA9LXBRY0

https://www.youtube.com/watch?v=rNbfCxJhRy4

https://www.youtube.com/watch?v=qPlQ0zSNen4
ɵ
Slope α R
Bigger the slop bigger is Resistance & temperature

ʎ
e-

u1 + u2 + u3 + ---- un = u Avg = 0

Vd = V avg = V1 +V2 + V3+ ------ Vn

e2

https://www.youtube.com/watch?v=f6J5i3HGfsU
https://www.youtube.com/watch?v=FTiyKKD5luE

Sunil jangra notes

https://www.youtube.com/watch?v=F1pVGrqR794
The Average velocity with which free electrons drifted to the opposite direction of applied
electric field

When conductor is subjected to an electric field E, each electron experience a force

https://www.youtube.com/watch?v=Y9_-7mMAH4w

https://www.youtube.com/watch?v=BQ9EzYy6fvg

Θ α

notes
https://www.youtube.com/watch?
v=Q5GBeMCr6Is&list=PLgRdr6oVccB6o2QVfl11X7_j_OGczYZfX&index=2
https://www.youtube.com/watch?v=z5h70KrDycM

Cube resitance
https://www.youtube.com/watch?v=dawXNEjpbBQ

https://www.youtube.com/watch?v=bDn8LpBcZ30

motion jee crash

https://www.youtube.com/playlist?list=PLZYt2g8epPyuRUXMFnEzmpCS0Rm6gTvxD

https://www.youtube.com/playlist?list=PLxyGaR3hEy3hlH58Stj9QlDuGyR3w7Nb9

cbse
https://www.cbse.gov.in/cbsenew/

https://www.cbse.gov.in/newsite/examination.html

paper
https://mycbseguide.com/cbse-question-papers.html

drift velocity
khan
https://www.youtube.com/watch?v=v-En7qY5vzY

Chapter-wise Physics Deleted Syllabus Class 12 CBSE 2024-

25

 Current Electricity
Resistivity of Various Materials, Carbon resistors, Colour code for carbon
resistor, Combinations of Resistors – Series and Parallel, Meter Bridge,
 Potentiometer.
Deleted Exercises 3.3, 3.4, 3.10, 3.12, 3.14–3.23

Jee 2021
The Colour coding on a carbon resistor is shown in the given figure.
The resistance value of the given resistor is :
(a) Draw a graph showing the variation of current versus voltage in an electrolyte when an
external resistance is also connected.
Ans-
a) When an external resistance is connected to an electrolyte then there is a voltage
drop in the resistance so the voltage across will reduce. When we plot a graph showing
the variation of current versus voltage it is a straight line with a lesser slope. It is due to
the presence of external resistance which implies for flowing the same current in the
circuit with external resistance require more voltage than the circuit without resistance.

(b) (i) The graph between resistance (R) and temperature (T) for Hg is shown in the figure (a).
Explain the behaviour of Hg near 4 K.
Here at 4 K temperature the resistance of Hg becomes zero which is the characteristic
shown by superconductors. So we can say that Hg behaves as superconductors at the
temperature of 4K

(ii) In which region of the graph shown in the figure (b) is resistance negative and why ?

From the graph, it shows that from B to C slope is >90 ie –ve, resistance is negative.
Here when voltage increases current is decreased which means resistance is negative.

https://www.youtube.com/watch?v=FTiyKKD5luE
https://www.youtube.com/watch?v=4oEwMpup4bo

Abhishek Sahu - physicswallah

https://www.youtube.com/playlist?list=PLIyq6M-A8_LxQP4MqRrKjVrnGqIytFhFA
KRICHHOF LAW