Class 11 — Notes 🔭

Electric charge is a fundamental property of matter. There are two types: positive and negative. Like charges repel and unlike charges attract.

Properties of charge:
1. Quantisation: Charge always comes in multiples of e = 1.6×10⁻¹⁹ C. So q = ne.
2. Conservation: Total charge of isolated system remains constant.
3. Additivity: Total charge = algebraic sum (with signs) of all charges.

Coulomb's Law: The force between two point charges is directly proportional to the product of charges and inversely proportional to square of distance.

F = kq₁q₂/r² = q₁q₂/(4πε₀r²)
k = 9×10⁹ Nm²/C², ε₀ = 8.85×10⁻¹² C²/Nm²

The region around a charge where another charge experiences a force is called the electric field.

E = F/q₀ (force on test charge per unit positive charge)
Due to point charge: E = kq/r². Unit: N/C or V/m. Vector quantity.

Electric field lines properties: (1) Start on + charge, end on − charge (2) Never intersect (3) Tangent = direction of E (4) Density = strength of field

Superposition principle: Total E at a point = vector sum of individual fields due to each charge.

Electric Potential (V): Work done per unit positive charge to bring a test charge from infinity to a point.
V = W/q₀ = kq/r. Unit: Volt (V) = J/C. Scalar quantity.

Relationship E and V: E = −dV/dr. Field directed from high to low potential.

Equipotential surface: V is same at every point on the surface.
(1) E is always perpendicular to equipotential surface
(2) No work done moving charge along equipotential surface
(3) For point charge: equipotential surfaces are concentric spheres

For conducting sphere of radius R:
Outside (r > R): V = kQ/r | Surface: V = kQ/R | Inside: V = kQ/R (constant)

A capacitor stores electric charge and energy. It has two conducting plates separated by insulating medium.

C = Q/V. Unit: Farad (F). 1F = 1C/V.

Parallel plate capacitor: C = ε₀A/d (in air)
With dielectric: C = Kε₀A/d (K = dielectric constant, K > 1)

Series: 1/C = 1/C₁ + 1/C₂ + ...
Parallel: C = C₁ + C₂ + ...

Energy stored: U = ½CV² = ½QV = Q²/2C

Dielectric: insulating material that increases capacitance by reducing E field inside by factor K. Examples: mica, glass, paper.

When many atoms come together in a metal like copper, the outermost electrons (valence electrons) become free — they are no longer attached to any particular atom. These are called free electrons or conduction electrons. They move randomly in all directions inside the metal.

Now imagine we connect a battery to a copper wire. The battery creates an electric field inside the wire. This field pushes the free electrons and they start flowing in one direction — this flow of charge is called Electric Current.

Definition: Electric current is the amount of charge flowing through a cross-section of a conductor per unit time.

Formula: I = q/t
where q = charge in Coulombs (C), t = time in seconds (s), I = current in Amperes (A)

If current is changing with time, we use: I(t) = lim(Δt→0) Δq/Δt

SI Unit: Ampere (A). Named after French physicist André-Marie Ampère.
1 Ampere = 1 Coulomb per second (1 A = 1 C/s)

Examples of current values:
• Lightning: up to 10,000 A
• Household appliances: a few Amperes
• Semiconductor devices: milliampere (mA), microampere (μA), nanoampere (nA)

Sign Convention: In a circuit, we draw current in the direction in which positive charges would move, even though in reality, it is the electrons (negative charges) that move in the opposite direction. This is just a convention we follow.

Without electric field: The free electrons in a metal move randomly in all directions with very high speeds (about 10⁶ m/s). But since they move in all random directions, there is no net movement in any particular direction — so NO current flows.

With electric field applied: When we connect a battery, an electric field is created inside the conductor. Now the electrons still move randomly, but they also slowly drift in the direction opposite to the electric field. This is called drift.

Drift Speed (Vd): The average velocity with which electrons move in a particular direction (opposite to field) due to the applied electric field is called drift speed.

Drift speed in copper ≈ 10⁻⁴ to 10⁻⁵ m/s — this seems very slow!
But don't get confused — the bulb lights up instantly when you press the switch because the electric field propagates at nearly the speed of light (3×10⁸ m/s), not because electrons travel fast.

Relationship between current and drift speed:
Consider a wire of cross-section A, with n = free electrons per unit volume, each having charge e.
In time t, electrons drift a distance L = Vd × t
Total charge q = n × A × L × e = nAVd·t·e
Current I = q/t = nAVde

Current density J = I/A = nVde
Drift velocity: Vd = I/nAe = J/ne
Unit of J = A/m²

In 1828, German scientist George Simon Ohm discovered a very important relationship between voltage and current in a conductor.

Statement of Ohm's Law: "The current I through a conductor is directly proportional to the potential difference V applied across its two ends, provided the physical state (temperature, material) of the conductor remains unchanged."

Mathematically: I ∝ V → V = IR

Here, R is called the Resistance of the conductor. It opposes the flow of current.

Unit of Resistance = Ohm (Ω)
1 Ω = 1 Volt / 1 Ampere
If a potential difference of 1V across a conductor produces a current of 1A, its resistance = 1Ω

Conductance (C) = 1/R — measures how easily current flows
Unit of conductance = Siemens (S) or Ω⁻¹

I-V graph: For an ohmic conductor, the graph of current (I) vs voltage (V) is a straight line passing through the origin. The slope of this line = 1/R.

Physical origin of Ohm's Law:
When electric field E is applied, electrons accelerate with acceleration a = eE/m.
They gain drift velocity Vd = aτ where τ = average time between collisions.
This gives: E = ρJ where ρ = m/ne²τ
Since m, n, e, τ are all constants for a material → ρ is constant → Ohm's law is obeyed.

Ohm's law is not obeyed by all materials. Based on the I-V graph, conductors are classified into two types:

1. Ohmic (Linear) Devices:
These follow Ohm's law. Their I-V graph is a straight line through origin. Resistance is constant regardless of voltage or current.
Examples: Nichrome wire, copper wire, silver wire, most metals

2. Non-Ohmic (Non-linear) Devices:
These do NOT follow Ohm's law. Their I-V graph is a curve, not a straight line. Resistance changes with voltage or current.
Examples: Liquid electrolytes, vacuum tubes, junction diodes, thermistors, LED

For non-linear devices, resistance at a particular point is defined as:
R = dV/dI (slope of tangent to I-V curve at that point)

Remember: The I-V graph of a diode is a perfect example of non-ohmic behaviour — it allows current in only one direction.

When current flows through a resistor, the electrons gain kinetic energy from the electric field. When they collide with the ion cores of the metal, they transfer this energy to the ions — the ions vibrate more — and the resistor heats up. This is called the heating effect of current (Joule heating).

Energy calculation:
When charge Q moves through potential difference V, work done = W = VQ
Since Q = I × t → W = VIt

Power (P) = Energy per unit time = W/t
P = IV = V²/R = I²R
Unit of power = Watt (W). 1W = 1 J/s

Commercial unit of energy:
In everyday life, energy is measured in kilowatt-hour (kWh)
1 kWh = 1000W × 3600s = 3.6 × 10⁶ J
This is what we call "1 unit" of electricity on our electricity bill.

Resistors are components used to control (limit) the flow of current in a circuit. Two main types:
1. Carbon resistors — small, inexpensive, used for high-value resistances
2. Wire wound resistors — used for low-value, precise resistances

Colour Code:
Carbon resistors have coloured bands to indicate their resistance value.
B B R O Y G B V G W = 0 1 2 3 4 5 6 7 8 9
Mnemonic: "B B Roy in Great Britain has Very Good Wife"

4-band code: 1st band = 1st digit | 2nd band = 2nd digit | 3rd band = multiplier | 4th band = tolerance
Gold = ×10⁻¹, ±5% | Silver = ×10⁻², ±10% | No colour = ±20%

Example: Yellow(4) Violet(7) Orange(×10³) Gold(±5%) = 47,000Ω = 47kΩ ±5%

Rheostat: A variable resistor whose resistance can be changed continuously. Used to control current, fan speed, brightness of lights, etc.

Series Combination:
When resistors are connected end-to-end in a single path:
• Same current flows through all resistors
• Voltage divides across resistors
• Rs = R1 + R2 + R3 + ...
• Equivalent resistance > any individual resistance

Parallel Combination:
When resistors are connected between the same two points:
• Same voltage across all resistors
• Current divides through each branch
• 1/Rp = 1/R1 + 1/R2 + 1/R3 + ...
• Equivalent resistance < smallest individual resistance

This is why household appliances are connected in parallel — each gets full 230V and works independently.

Experiment shows that the resistance R of a wire depends on:
1. Length (l): R ∝ l — longer wire = more resistance (more obstacles for electrons)
2. Area (A): R ∝ 1/A — thicker wire = less resistance (more paths for electrons)
3. Material: Different materials have different resistances for same dimensions

Combining: R = ρl/A
where ρ (rho) = Resistivity (also called Specific Resistance)

Resistivity ρ = RA/l
SI Unit: Ohm-metre (Ω·m)

Resistivity is a property of the material, not of a particular object. Resistance depends on shape and size; resistivity does not.

Conductivity σ = 1/ρ. Unit: Sm⁻¹

Resistivity values (at room temperature):
• Silver: 1.59×10⁻⁸ Ω·m (best conductor)
• Copper: 1.72×10⁻⁸ Ω·m (most used conductor)
• Nichrome: 100×10⁻⁸ Ω·m (used in heaters)
• Silicon: 3×10⁴ Ω·m (semiconductor)
• Glass: 10¹¹–10¹³ Ω·m (insulator)

The resistivity of a material changes with temperature. For metals, as temperature increases, the atoms vibrate more — electrons collide more frequently — so resistance increases.

The relationship is approximately linear over a range of temperatures:
ρ = ρ₀[1 + α(T − T₀)]
Similarly: R = R₀[1 + α(T − T₀)]

where:
• R₀ = resistance at reference temperature T₀ (usually 0°C)
• R = resistance at temperature T
• α = Temperature Coefficient of Resistance

α = (R − R₀) / [R₀ × (T − T₀)]
Unit: per degree Celsius (°C⁻¹) or per Kelvin (K⁻¹)

For metals: α is positive (resistance increases with temperature)
For semiconductors and insulators: α is negative (resistance decreases with temperature)

Superconductivity:
In some metals and alloys, when temperature is reduced below a certain value called Critical Temperature (Tc), the resistivity suddenly drops to exactly zero. This phenomenon is called Superconductivity.

Example: Mercury becomes superconducting at Tc = 4.2K

Applications of superconductors:
• Superconducting magnets (produce very strong magnetic fields — a few Tesla)
• NMR (Nuclear Magnetic Resonance) spectrometers
• MRI (Magnetic Resonance Imaging) machines in hospitals

EMF Device: Any device that maintains a potential difference (voltage) between two points to keep current flowing in a circuit. Examples: Battery, solar cell, generator, fuel cell.

EMF (Electromotive Force) ε: The work done by the EMF device per unit charge to move charge from negative terminal to positive terminal inside the device.
ε = dW/dq. Unit: Joule/Coulomb = Volt (V)

Internal Resistance (r): The resistance offered by the electrolyte/material inside the cell itself. Even a battery has some resistance inside it.

Terminal Voltage: The actual voltage available at the terminals of a cell when current flows.
V = ε − Ir (terminal voltage < EMF when discharging)

Current in circuit: I = ε/(R + r)
where R = external resistance, r = internal resistance

Maximum current is obtained when R = 0 (short circuit):
I_max = ε/r

Cells in Series:
Positive terminal of one connected to negative of next.
εeq = ε₁ + ε₂ + ... (EMFs add up)
req = r₁ + r₂ + ... (internal resistances add up)
Advantage: Higher total voltage. Can identify damaged cells easily.

Cells in Parallel:
All positive terminals connected together, all negative terminals connected together.
1/req = 1/r₁ + 1/r₂ + ... (reciprocals add)
Advantage: Circuit continues to work even if one cell fails. Current capacity increases.
Disadvantage: Total voltage cannot be increased.

Types of Cells:
1. Primary cells: Cannot be recharged. Use once and discard. Example: Dry cell, alkaline cell. Cheap and light. Not for heavy loads.
2. Secondary cells: Can be recharged many times. Example: Lead acid battery (used in cars), lithium-ion battery (mobiles), solar cell.
3. Fuel cells: Use hydrogen as fuel. Reaction produces electricity + water. No CO₂ emission → environment friendly. Used in fuel cell vehicles (FCV).

Magnetism was known since ancient times (before 600 B.C.), but scientific understanding began with William Gilbert who discovered that Earth itself is a weak magnet.

Magnetic lines of force are imaginary lines that show the direction and strength of the magnetic field. They go from North pole to South pole outside the magnet, and South to North inside — forming closed loops (unlike electric lines which start and end on charges).

Magnetic flux φ = B × A (for uniform field perpendicular to area)
Magnetic field B = φ/A. Unit: Tesla (T) = Weber/m². 1T = 10⁴ Gauss

A bar magnet has pole strength +qm at North and −qm at South. Since it has two equal opposite poles, it is called a magnetic dipole — just like an electric dipole.

Magnetic dipole moment m = qm × 2l (vector from S pole to N pole)

Axial field (point on axis): Ba = (μ₀/4π)(2m/r³) — in direction of m
Equatorial field (point on equator): Beq = (μ₀/4π)(m/r³) — opposite to m
Important: Baxis = 2 × Beq at the same distance r

For a point at angle θ: B = (μ₀m/4πr³)√(3cos²θ+1)

Gauss' law for magnetism: The net magnetic flux through any closed Gaussian surface is always ZERO.
ΦB = ∮B·dS = 0

This is because magnetic monopoles do not exist. Every magnet always has both North and South poles. So the same number of field lines that enter a closed surface also leave it — net flux = 0.

This is different from electrostatics where ΦE = q/ε₀ (can be non-zero if a charge is enclosed).

Conclusion: Only magnetic dipoles exist in nature, never a single pole (monopole).

A freely suspended magnet always aligns N-S — this shows Earth has a magnetic field everywhere. This is called Terrestrial Magnetism. It is very useful for navigation using a compass.

Earth behaves like a huge bar magnet:
• Magnetic North pole (N) is below Antarctica
• Magnetic South pole (S) is below north Canada
• Magnetic equator passes through India near Thiruvananthapuram

Three elements of Earth's magnetism:
1. Magnetic Declination (D): angle between geographic and magnetic meridian
2. Angle of Dip (I): angle of resultant B with horizontal. 0° at equator, 90° at poles
3. Horizontal component BH: BH = BcosI, BV = BsinI, tanI = BV/BH, B = √(BV²+BH²)