CLASS 12 CURRENT ELECTRICITY
CURRENT ELECTRICITY
✤ ELECTRIC CURRENT
Flow of electric charges through a conductor constituent an electric current
I = Q/t (Ampere)
Scalar quantity
❈ Period of revolution of the electrons is T = 2πr / v
Frequency of revolution v = 1/T = v/2πr
Current at any point of the orbit is
I = ev = ev/2πr
✤ Electromotive Force (EMF):
Source may be defined as the work done by the source in taking a unit positive change from lower to the higher potential.
ε = W total/Q (Volt)
1. ε = I(R+r)
2. ε = V+Ir or V=ε-Ir
3. I = ε/R+r
✤ Ohm's Law
Current flowing through a conductor is directly ∝ to P.D applied across
As ends, provided the temp & other physical conditions remains unchanged.
(Ω)(ohm) V=RI Resistance.
Its Depends on.
i) Independent of V & I
ii) Depends on nature of conductor, lengths & area of cross-section & physical condition temp. etc.
Any material that has some resistance is called a resistor.
Symbols of resistors & meters.
❈ Resistivity or Specific Resistance - of a material may be defined as the resistance of a conductor of that material, having unit length & unit area of
cross-section.
ρ = R A / l (ohm meter) (Ωm)
Resistance: obstacle produced by the conductor in the path of e-
R = ρ l/A
If a wire is stretched then, A₁l₁ = A₂l₂ and ratio of new and old resistance
R₂ / R₁ = l2/l1 x A₁/A₂
OR, R₂ / R₁ = (l₂/l₁)² = (A₁/A₂)²
Note: when cross-section area is different in a wire then 𝛸 = dθ/dt
Remains constant at every cross-section.
Note: Resistance is arise due to frequent collision of free electrons with
The ions or atoms in wire.
Resistance as human body is 10⁵ Ω, in wet condition it is 1500 Ω.
❈ Current density: at any point inside a conductor is defined as the amount of charge flowing per second through a unit area held normal to the
direction of the flow of charge at that point.
𝑗 = 𝐼/𝐴 (Am⁻²) [AL⁻²]
❈ Relation b/w 𝐸 and 𝐽: 𝐸 = 𝛾 𝐽
𝜎𝐸 = 𝑗 in conductivity.
❈ Conductance: The conductance of a conductor is the ease with which electric charges flow through it. It is equal to the reciprocal of its resistance
G = 1/R (ohm⁻¹, mho, Siemens(s))
❈ Conductivity: The reciprocal of the resistivity of a material is called its conductivity.
𝜎 = 1/𝜌 (ohm⁻¹m⁻¹, mhom⁻¹, Sm⁻¹)
:. 𝜌 ∝ 1/𝑛, 𝑛→number density of 𝑒⁻ 𝜌 ∝ 1/𝜏, 𝜏→relaxation time.
❈ Drift Velocity: It may be defined as the average velocity gained by the free electrons of a conductor in the opposite direction of the externally
applied electric field.
V𝑑 = 𝑒𝐸𝜏/m ---> T = relaxation time
❈ Relation b/w I & Vd → Relation b/w j & Vd →
I = enAVd j = envd
number of electrons / unit current density
❈ Mobility of Charge Carriers:
Mobility of a charge carries is the drift velocity acquired by it in a unit electric field.
μ = Vd / E (m²V⁻¹s⁻¹) mobility is always +ve for both charge
μ = -e.t/m ---> Relaxation time carrier.
✤ Temperature depends on Resistivity in metal-
Pt = P₀ [1+α(T₂-T₁) ] Rt = R₀[1+α(T₂-T₁)]
α = Rb - R₀ / R₀ X (T₂-T₁)
α = Pt - P₀ / P0(T2-T1)
Graphs 𝜌 vs Temp
1) COPPER 2) NICHORME 3) SEMICONDCUTOR
§ Alloys have high resistivity. (10⁻⁶ Ωm - 10⁻⁴ Ωm)
2- less temp. coefficient.
❈ Use of alloys in making standard resistors:
i) Have high value of resistivity.
ii) Very small temperature coefficient.
iii) Least affected by atomospheric conditions like air, moisture.
iv) Their contact potential with copper is small.
❈ Resistance in Series
Rs = R1 + R2 + ... + Rn
Power (P) = P1P2 / P1 + P2
Laws of resistance in series
- Current through each resistance is same.
- Total potential drop = Sum of potential drops across the individual R.
- Individual potential drop ∝ individual resistance.
- Equivalent R = Sum of individual R
- Equivalent resistance is larger than the largest individual R.
1. V = V1 + V2 + V3
2. I = V / (R1+R2+R3)
3. V1 = IR1, V2 = IR2, V3 = IR3
❈ Resistance in Parallel
1 / Rp = 1/ R1 + 1/ R2 + ... + 1 / Rn
Power (Pp) = P1P2 / P1 + P2
Laws of resistance in parallel.
- Potential drop across each R is same.
- Total current = Sum of current through individual resistances.
- Individual I ∝ individual R
- Reciprocal of equivalent resistance = Sum of the reciprocal of the individual R.
- Equivalent resistance < smallest individual R.
I₁=V/R₁ I₂=V/R₂ I₃=V/R₃
❈ Internal Resistance of a cell
The resistance offered by the electrolyte of a cell to the flow of current b/w its electrodes is called internal resistance of the cell.
Depends on:-
- Nature of electrolyte.
- α concentration of the electrolyte.
- α distance b/w 2 electrodes.
- inversely α Common area of the electrodes
- immersed in the electrolyte.
- ↑es with tes temp of electrolyte.
❈ Terminal Potential difference (V)
The potential drop across the terminals of a cell when a current is being drawn from it is called its terminal potential difference
Relation b/w r, ε, V
V=IR = εR / R+r V = ε-Ir
Note: output power is maximum
when internal resistance = Ext. resistance
r=R
Combination of cells in Series & Parallel
Combination of cells is called a battery.
❈ Notes: 1. in open circuit, E=V.
2. during charging, net p.d. of circuit = V-E
3. Voltage drop = I.r. = V-E (It is also called LOST VOLTAGE)
✤ Cell in series
When -ve terminal of 1 cell is connected to the +ve terminal of the other cell and so on, the cells are said to be connected in series.
Eeq = E₁ + E₂ & req = r₁ + r₂
Note: If any one or two cell are
connected in wrong way then we
have to subtract their emf from
others.
✤ Cell in parallel
When +ve per terminal of all cells are connected in parallel to 1 point & all their -ve terminals to another points, the cells are said to be connected in parallel.
Eeq = E₁r₂ + E₂r₁/r1+r2 & req = r₁ r₂ / r1+r2
Eeq/req = E₁ + E₂ & req = 1/r₁ + 1/r₂
Eeq = ( E₁/r₁ + E₂/r₂ ) / [1/r1 + 1/r2]
❈ Healing Effect of Current
The phenomenon of the production of heat in a resistor by the flow of an electric current through it is called heating effect of current of for Joule heating
❆ Heat Produced by Electric Current: [Joule's Law]
According to Joule's Law the heat produced in a resistor is: - α Bag Square of current for a given R
- α to the resistance R for a given l.
- inversely α to the resistance R for given V.
- α to the time for which the current flows through the resistor.
H=IVt = T²Rt = V²/R (Joule)
H= VIt/4.18 = T²Rt/4.18 = V²/4.18R (Cal)
❈ Electric Power
The rate at which an appliance converts electric energy into other forms of energy is called its electric power.
Work done or energy consumed = W=VIt (Joule)
Electric Power = P=W/t = VI=T²R=V²/R (Watt)
1 kilowatt = 1000W & 1 Megawatt=10⁶W
❈ Electric Energy
Total work done by the source of emf in maintaining an electric current in a circuit for a given time is called electric energy consumed in the circuit.
1 Joule = 1 volt x 1 ampere x 1 second = 1 watt x 1 second
1 kWh = 3.6 x 106 J
1 Wh = 3.6 x 103 J
✤ Kirchhoff's Laws
1) Electric network
Term electric network is used for a complicated system of electrical conductors.
2) Junction
Any point in an electric circuit where 2 or more conductors are joined together is a junction.
3) Loop on Mesh
Any closed conducting path in an electric network is called a loop or mesh.
4) Branch
A branch is any part of the network that lines b/w 2 junctions.
Kirchhoff's first law on Junction rule.
In an electric circuit, the algebraic sum of currents at any junction is zero. Σ I = 0
Sign convention
1) The I flowing towards the junction are taken as +ve.
2) I flowing away from junction are taken as -ve
Incoming current = Outgoing current
Note: It is based on conservation of charge. i.e.
Σq=constant
2. It is applicable for open and closed circuit.
Kirchhoff's Second Law / Loop rule.
Algebraic sum of the emfs in any loop of a circuit is equal to the sum of the products of currents & R in it. i.e. ΣV=0
ΣE=ΣIR. Note: It is based on conservation of energy.
Sign Convention:
Can take any direction as the direction of traversal. emf is taken as +ve if the direction of traversal is from its -ve to the positive terminal.
✤ Wheatstone Bridge
Arrangement of 4 R used to determine 1 of these R quickly & accurately in terms of the remaining 3 R.
Principle: Based on the fact that, if G shows null then ---
P/Q=R/S
Note: It is based on null deflection
Notes: [1] It is most sensitive when resistance in 4 arms are of same order.
[2] It is not suitable for very low and very high resistance.
[3] In balanced condition, No effect of interchanging the position of battery and G.
When 'n' identical cells of each emf ε are connecting in Parallel then
Total Emf = E
And in the case of series, Total emf = nE
When one cell is wrongly connected in series then
total emf = nE-2E
and total internal resistance = nR (No effect)
for maximum voltage → cells are in series
for maximum current → cells are in parallel
for maximum Power → cells are in mixed grouping
RAB = R1 (R1+3R2)/ (R2 +3R1)
* * * * * * * * * * * * * *
