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⚡

Electricity

Class 12 Physics Concepts

Master the Flow of Electric Charge

📋 Chapter Overview

Electric Charges and Fields
Electric Potential and Potential Difference
Capacitance and Capacitors
Current Electricity and Ohm’s Law
Electrical Networks and Kirchhoff’s Laws
Heating Effect of Electric Current
Electric Power and Energy

⚡ Electric Charge

Fundamental Property of Matter

Q = ne

Where: Q = charge, n = number of electrons, e = 1.6 × 10⁻¹⁹ C

Two types: Positive and Negative charges
Like charges repel, unlike charges attract
Charge is quantized and conserved
SI unit: Coulomb (C)

🔬 Coulomb’s Law

Force Between Two Point Charges

F = k(q₁q₂)/r²

Where: k = 9 × 10⁹ Nm²/C², r = distance between charges

Force is directly proportional to product of charges
Force is inversely proportional to square of distance
Force acts along the line joining the two charges
Permittivity of free space: ε₀ = 8.85 × 10⁻¹² C²/Nm²

🌐 Electric Field

Electric Field Intensity

E = F/q = kQ/r²

Unit: N/C or V/m

Electric field is a vector quantity
Direction: from positive to negative charge
Electric field lines never intersect
Stronger field → closer field lines

⚡ Electric Potential

Potential at a Point

V = W/q = kQ/r

Unit: Volt (V) = Joule/Coulomb

Electric potential is a scalar quantity
Work done to bring unit positive charge from infinity
Potential difference = V₁ – V₂
Equipotential surfaces have same potential

🔗 Relationship: Electric Field & Potential

Field and Potential Connection

E = -dV/dr

For uniform field: E = V/d

Electric field points from higher to lower potential
Electric field is negative gradient of potential
No electric field along equipotential surface
Work done in moving charge along equipotential = 0

🔋 Capacitance

Capacity to Store Charge

C = Q/V

Unit: Farad (F) = Coulomb/Volt

Capacitance depends on geometry and medium
For parallel plate: C = ε₀A/d
With dielectric: C = Kε₀A/d
Energy stored: U = ½CV² = ½QV = ½Q²/C

🔌 Capacitor Combinations

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Series

1/C = 1/C₁ + 1/C₂ + …

Same charge, different voltages

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Parallel

C = C₁ + C₂ + …

Same voltage, different charges

🌊 Current Electricity

Electric Current

I = Q/t = nAve

Unit: Ampere (A) = Coulomb/second

Current is rate of flow of charge
Conventional current: positive to negative
Electron flow: negative to positive
Current density: J = I/A = nve

⚖️ Ohm’s Law

Fundamental Law of Electricity

V = IR

Where: V = Voltage, I = Current, R = Resistance

Valid for ohmic conductors at constant temperature
V-I graph is a straight line through origin
Resistance: R = ρL/A
Resistivity (ρ) is material property

🔗 Resistance Combinations

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Series

R = R₁ + R₂ + …

Same current, different voltages

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Parallel

1/R = 1/R₁ + 1/R₂ + …

Same voltage, different currents

⚖️ Kirchhoff’s Laws

🔄

Current Law (KCL)

ΣI = 0

Sum of currents at a node = 0

🔁

Voltage Law (KVL)

ΣV = 0

Sum of voltages in a loop = 0

⚡ Electrical Power

Rate of Energy Consumption

P = VI = I²R = V²/R

Unit: Watt (W) = Joule/second

Power is rate of energy transfer
Energy consumed: E = Pt
Commercial unit: kWh (kilowatt-hour)
Maximum power transfer when R = r (internal resistance)

🔥 Heating Effect of Current

Joule’s Law of Heating

H = I²Rt = VIt = V²t/R

Unit: Joule (J)

Heat produced is proportional to I²Rt
Applications: Electric heater, bulb, fuse
In series: H ∝ R (more resistance, more heat)
In parallel: H ∝ 1/R (less resistance, more heat)

🔋 Electric Cell

EMF and Terminal Voltage

V = ε – Ir

Where: ε = EMF, r = internal resistance

EMF (ε): Maximum potential difference
Terminal voltage decreases with current
Internal resistance causes voltage drop
Short circuit current: I = ε/r

🔋 Cell Combinations

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Series

ε = ε₁ + ε₂ + …

r = r₁ + r₂ + …

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Parallel

ε = ε₁ = ε₂ = …

1/r = 1/r₁ + 1/r₂ + …

⚖️ Wheatstone Bridge

Balanced Condition

R₁/R₂ = R₃/R₄

No current through galvanometer

Used to measure unknown resistance accurately
Bridge is balanced when galvanometer shows zero deflection
At balance: P/Q = R/S
Sensitivity depends on galvanometer and bridge ratio

📏 Potentiometer

Principle

V ∝ L

Potential difference ∝ Length of wire

Based on null deflection method
No current drawn from test circuit
Used to measure EMF, potential difference, and internal resistance
More accurate than voltmeter

🌡️ Temperature Dependence of Resistance

Temperature Coefficient

R = R₀(1 + αΔT)

α = temperature coefficient of resistance

Metals: Resistance increases with temperature (α > 0)
Semiconductors: Resistance decreases with temperature (α < 0)
Superconductors: Zero resistance below critical temperature
Applications: Temperature sensors, RTD

🕸️ Electric Networks

Node: Junction of three or more conductors
Branch: Path between two nodes
Loop: Closed path in a circuit
Mesh: Loop with no other loops inside
Use KCL at nodes and KVL in loops
Number of independent equations = (nodes – 1) + meshes

🏃 Drift Velocity

Average Velocity of Electrons

vd = I/(nAe)

Where: n = electron density, A = area, e = electron charge

Typical drift velocity: ~10⁻⁴ m/s
Much slower than random thermal velocity
Current flows instantly due to electric field propagation
Mobility: μ = vd/E

⚡ Conductivity and Resistivity

Material Properties

σ = 1/ρ = nμe

σ = conductivity, ρ = resistivity, μ = mobility

Conductivity: Ability to conduct current
Resistivity: Intrinsic property of material
Good conductors: ρ ~ 10⁻⁸ Ωm
Insulators: ρ ~ 10¹² – 10¹⁶ Ωm

🎨 Carbon Resistors – Color Code

Color Code System:

Black: 0, Brown: 1, Red: 2

Orange: 3, Yellow: 4, Green: 5

Blue: 6, Violet: 7, Grey: 8

White: 9, Gold: ±5%, Silver: ±10%

Reading: First two bands = significant figures, Third band = multiplier, Fourth band = tolerance

📝 Key Formulas Summary

Coulomb’s Law: F = kq₁q₂/r²

Electric Field: E = F/q = kQ/r²

Electric Potential: V = kQ/r

Capacitance: C = Q/V

Ohm’s Law: V = IR

Power: P = VI = I²R = V²/R

Joule’s Heating: H = I²Rt

Drift Velocity: vd = I/(nAe)

📐 Important Units & Constants

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Charge

Coulomb (C)

e = 1.6 × 10⁻¹⁹ C

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Potential

Volt (V)

1 V = 1 J/C

🌊

Current

Ampere (A)

1 A = 1 C/s

🛡️

Resistance

Ohm (Ω)

1 Ω = 1 V/A

k = 9 × 10⁹ Nm²/C², ε₀ = 8.85 × 10⁻¹² C²/Nm²

🔬 Real-World Applications

Capacitors: Energy storage, filters, timing circuits
Resistors: Current limiting, voltage division, heating
Batteries: Portable power sources, electric vehicles
Superconductors: MRI machines, power transmission
Semiconductors: Electronics, computers, solar cells
Electric Power: Household appliances, industrial motors

💡 Problem Solving Strategy

Draw clear circuit diagrams with proper labeling
Identify series and parallel combinations
Apply Kirchhoff’s laws systematically
Use appropriate formulas for power calculations
Check units and dimensional consistency
Verify answers using different methods when possible
Practice numerical problems regularly

⚠️ Common Mistakes to Avoid

Confusing series and parallel resistance formulas
Mixing up current direction in circuits
Forgetting internal resistance of batteries
Incorrect application of Kirchhoff’s laws
Wrong power formula selection
Unit conversion errors
Sign errors in potential calculations

🎯 Exam Preparation Tips

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Theory

Understand concepts clearly

Derive important formulas

🧮

Numericals

Practice variety of problems

Master formula applications

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Graphs

V-I characteristics

Power curves

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Experiments

Wheatstone bridge

Potentiometer

🎊 Summary

Electricity governs the behavior of charged particles
Electric field and potential are fundamental concepts
Ohm’s law and Kirchhoff’s laws solve circuit problems
Power and energy calculations are crucial
Understanding applications enhances learning
Regular practice leads to mastery

🌟 Keep Exploring the Electric World! 🌟

Master these concepts for success in physics and engineering!