Current Electricity and Circuits

• Current Electricity: Deals with the flow of electric charge through conductors.

Electric Current

• Defined as the rate of flow of electric charge through a conductor.
• Measured in Amperes (A).
• Current (I) = Charge (Q) / Time (t).
• Drift velocity is the average velocity attained by charged particles in a material due to an electric field.

Ohm's Law

• States that the potential difference (V) across a conductor is directly proportional to the current (I) flowing through it, given the temperature remains constant.
• V = IR, where R is the resistance.
• Resistance is the opposition to the flow of electric current.
• Resistivity is a material property that quantifies how strongly a material opposes the flow of electric current.
• Conductance is the reciprocal of resistance, measuring how easily current flows.
• Conductivity is the reciprocal of resistivity, indicating how well a material conducts electricity.

Series and Parallel Circuits

• In series circuits, the total resistance is the sum of individual resistances (R = R1 + R2 + ...).
• The current remains the same through each resistor in a series circuit.
• In parallel circuits, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances (1/R = 1/R1 + 1/R2 + ...).
• The voltage remains the same across each resistor in a parallel circuit.

Electrical Energy and Power

• Electrical energy is the energy associated with electric charge.
• Electrical power is the rate at which electrical energy is consumed or generated.
• Power (P) = VI = I^2R = V^2/R.
• Electrical energy (E) = Pt.

Cells, EMF, Internal Resistance

• EMF (electromotive force) is the potential difference across the terminals of a cell when no current is drawn.
• Internal resistance is the resistance offered by the cell itself to the flow of current.
• Terminal voltage (V) = EMF (E) - Ir, where r is the internal resistance.

Kirchhoff's Laws

• Kirchhoff's Current Law (KCL): The total current entering a junction is equal to the total current leaving it.
• Kirchhoff's Voltage Law (KVL): The algebraic sum of the potential differences in a closed loop is zero.

Wheatstone Bridge

• An electrical circuit used to measure an unknown resistance.
• Balanced when the ratio of resistances in one branch equals the ratio in the adjacent branch (R1/R2 = R3/R4).

Potentiometer

• A device used to measure the potential difference accurately.

• Can be used to compare EMFs of two cells or to determine the internal resistance of a cell.

• Moving Charges and Magnetism: Explores the magnetic effects of moving charges and magnetic fields.

Magnetic Force

• A charge q moving with velocity v in a magnetic field B experiences a force F = q(v x B).
• The direction of the force is perpendicular to both the velocity and the magnetic field.
• The magnitude of the force is F = qvBsinθ, where θ is the angle between v and B.

Motion in a Magnetic Field

• When a charged particle enters a magnetic field perpendicularly, it moves in a circular path.
• Radius of the circular path (r) = mv/qB.
• Frequency of revolution (f) = qB/2πm.

Magnetic Field due to Current

• Biot-Savart Law: Gives the magnetic field dB at a point due to a small current element Idl.
• dB = (μ0/4π) (Idl x r)/r^3, where μ0 is the permeability of free space.

Magnetic Field due to a Straight Wire

• Magnetic field (B) at a distance r from a long straight wire carrying current I is B = (μ0I)/2πr.

Magnetic Field due to a Circular Loop

• Magnetic field at the center of a circular loop of radius R carrying current I is B = (μ0I)/2R.
• Magnetic field on the axis of a circular loop at a distance x from the center is B = (μ0IR^2)/2(R^2 + x^2)^(3/2).

Ampere's Circuital Law

• The line integral of the magnetic field B around any closed loop is equal to μ0 times the total current I threading the loop.
• ∮ B.dl = μ0I.

Solenoid and Toroid

• Solenoid: A long coil of wire carrying current. The magnetic field inside a solenoid is uniform and given by B = μ0nI, where n is the number of turns per unit length.
• Toroid: A doughnut-shaped coil of wire. The magnetic field inside a toroid is B = (μ0NI)/2πr, where N is the total number of turns and r is the radius of the toroid.

Force between Parallel Currents

• Two parallel wires carrying currents in the same direction attract each other.
• Two parallel wires carrying currents in opposite directions repel each other.
• Force per unit length between two parallel wires is F/L = (μ0I1I2)/2πd, where d is the distance between the wires.

Torque on a Current Loop

• A current loop placed in a magnetic field experiences a torque.
• Torque (τ) = MBsinθ, where M is the magnetic dipole moment and θ is the angle between M and B.
• Magnetic dipole moment (M) = NIA, where N is the number of turns, I is the current, and A is the area of the loop.

Moving Coil Galvanometer

• A device used to detect and measure small electric currents.

• Principle: A current-carrying coil placed in a magnetic field experiences a torque.

• Conversion of galvanometer into ammeter: By connecting a low resistance (shunt) in parallel with the galvanometer.

• Conversion of galvanometer into voltmeter: By connecting a high resistance in series with the galvanometer.

• Magnetism and Matter: Focuses on magnetic properties of materials.

Magnetic Dipole

• A magnetic dipole consists of two opposite magnetic poles separated by a small distance.
• Magnetic dipole moment (M) = m * 2l, where m is the pole strength and 2l is the distance between the poles.

Magnetic Field Lines

• Represent the direction and strength of the magnetic field.
• Magnetic field lines form closed loops.

Bar Magnet

• Behaves like a magnetic dipole.
• Magnetic field due to a bar magnet at an axial point: B = (μ0/4π) (2M/r^3).
• Magnetic field due to a bar magnet at an equatorial point: B = (μ0/4π) (M/r^3).

Earth's Magnetism

• Earth behaves as a giant magnet.
• Magnetic declination: The angle between the magnetic north and the true north.
• Magnetic dip (inclination): The angle between the Earth's magnetic field and the horizontal.
• Horizontal component of Earth's magnetic field (BH) = Bcosδ, where δ is the magnetic dip angle.

Magnetic Properties of Materials

• Diamagnetic materials: Weakly repelled by magnetic fields. They have no permanent magnetic dipoles.
• Paramagnetic materials: Weakly attracted by magnetic fields. They have permanent magnetic dipoles that align with the field.
• Ferromagnetic materials: Strongly attracted by magnetic fields. They can be permanently magnetized.
• Hysteresis: The lagging of magnetization behind the magnetizing field.

Magnetic Susceptibility and Permeability

• Magnetic susceptibility (χ): A measure of how easily a material can be magnetized.

• Relative permeability (μr): The ratio of the permeability of a material to the permeability of free space (μr = 1 + χ).

• Curie temperature: The temperature above which a ferromagnetic material loses its ferromagnetic properties and becomes paramagnetic.

• Electromagnetic Induction: Studies the production of EMF and current due to changing magnetic fields.

Faraday's Law of Electromagnetic Induction

• The induced EMF in any closed circuit is equal to the negative of the time rate of change of magnetic flux through the circuit.
• EMF (ε) = -dΦ/dt, where Φ is the magnetic flux.
• Magnetic flux (Φ) = B.A = BAcosθ, where B is the magnetic field, A is the area, and θ is the angle between B and A.

Lenz's Law

• The direction of the induced EMF is such that it opposes the change that produces it.

Motional EMF

• The EMF induced in a conductor moving in a magnetic field.
• EMF (ε) = Blv, where B is the magnetic field, l is the length of the conductor, and v is the velocity.

Induced Electric Fields

• A changing magnetic field produces an electric field.

Inductance

• The property of a coil to oppose any change in the current flowing through it.
• Self-inductance (L): When a changing current in a coil induces an EMF in the same coil.
• Mutual inductance (M): When a changing current in one coil induces an EMF in a neighboring coil.

Energy Stored in an Inductor

• Energy (U) = (1/2)LI^2, where L is the inductance and I is the current.

AC Generator (Alternator)

• A device that converts mechanical energy into electrical energy.

• Principle: Electromagnetic induction.

• EMF generated (ε) = NBAωsin(ωt), where N is the number of turns, B is the magnetic field, A is the area, and ω is the angular velocity.

• Alternating Current: Deals with AC circuits and their behavior.

AC Voltage and Current

• AC voltage and current vary sinusoidally with time.
• V = V0sin(ωt), where V0 is the peak voltage and ω is the angular frequency.
• I = I0sin(ωt), where I0 is the peak current.

Root Mean Square (RMS) Value

• The effective value of AC voltage or current.
• VRMS = V0/√2.
• IRMS = I0/√2.

AC Circuits with Resistors, Inductors, and Capacitors

• Resistor: Voltage and current are in phase.
• Inductor: Voltage leads the current by π/2.
• Capacitor: Current leads the voltage by π/2.

Reactance

• Opposition to the flow of AC current due to inductors and capacitors.
• Inductive reactance (XL) = ωL.
• Capacitive reactance (XC) = 1/ωC.

Impedance

• The total opposition to the flow of AC current in a circuit, including resistance and reactance.
• Impedance (Z) = √(R^2 + (XL - XC)^2).

Series LCR Circuit

• A circuit containing an inductor, capacitor, and resistor in series.
• Resonance: Occurs when XL = XC, and the impedance is minimum.
• Resonant frequency (ω0) = 1/√(LC).

Power in AC Circuits

• Average power (P) = VRMS IRMS cosφ, where cosφ is the power factor.
• Power factor (cosφ) = R/Z.

Transformers

• Devices used to increase or decrease AC voltage.

• Principle: Mutual induction.

• Voltage ratio (VS/VP) = Turns ratio (NS/NP) = Current ratio (IP/IS).

• Efficiency (η) = (Output power)/(Input power).

• Electromagnetic Waves: Discusses the nature and properties of electromagnetic waves.

Electromagnetic Waves

• Waves produced by oscillating electric and magnetic fields.
• EM waves are transverse in nature.
• EM waves do not require a medium to propagate.

Properties of Electromagnetic Waves

• Speed of EM waves in vacuum (c) = 1/√(μ0ε0) ≈ 3 x 10^8 m/s.
• Electric field (E) and magnetic field (B) are perpendicular to each other and to the direction of propagation.
• The energy in EM waves is equally divided between electric and magnetic fields.

Electromagnetic Spectrum

• The range of all possible frequencies of EM radiation.
• Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.

Uses of Electromagnetic Waves

• Radio waves: Communication.

• Microwaves: Cooking, radar.

• Infrared: Thermal imaging, remote controls.

• Visible light: Vision, photography.

• Ultraviolet: Sterilization, detecting forged documents.

• X-rays: Medical imaging.

• Gamma rays: Cancer treatment.

• Ray Optics and Optical Instruments: Covers reflection, refraction, and optical instruments.

Reflection of Light

• The bouncing back of light when it strikes a surface.
• Laws of reflection: Angle of incidence equals angle of reflection. The incident ray, reflected ray, and normal lie in the same plane.

Refraction of Light

• The bending of light as it passes from one medium to another.
• Snell's law: n1sinθ1 = n2sinθ2, where n1 and n2 are the refractive indices of the two media.

Total Internal Reflection

• Occurs when light travels from a denser to a rarer medium at an angle of incidence greater than the critical angle.

Lenses

• Transparent materials that refract light to form images.
• Lens maker's formula: 1/f = (n-1)(1/R1 - 1/R2), where f is the focal length, n is the refractive index, and R1 and R2 are the radii of curvature.

Optical Instruments

• Simple microscope, compound microscope, telescope.

• Magnifying power: The ratio of the angle subtended by the image at the eye to the angle subtended by the object at the eye.

• Wave Optics: Explores wave phenomena like interference, diffraction, and polarization.

Wavefront

• A surface of constant phase.

Huygens' Principle

• Every point on a wavefront acts as a source of secondary wavelets.

Interference

• The superposition of two or more waves to form a resultant wave of greater or lower amplitude.
• Constructive interference: Occurs when the path difference is an integral multiple of the wavelength (Δx = nλ).
• Destructive interference: Occurs when the path difference is an odd multiple of half the wavelength (Δx = (2n+1)λ/2).

Young's Double Slit Experiment

• Demonstrates the interference of light waves.
• Fringe width (β) = λD/d, where λ is the wavelength, D is the distance between the screen and the slits, and d is the distance between the slits.

Diffraction

• The bending of waves around obstacles or apertures.
• Single slit diffraction: The central maximum is twice as wide as the other maxima.

Resolving Power of Optical Instruments

• The ability of an optical instrument to distinguish between two closely spaced objects.

Polarization

• The restriction of the vibrations of a transverse wave to one direction.

• Brewster's law: When light is incident at the polarizing angle, the reflected and refracted rays are perpendicular to each other (tan ip = n).

• Dual Nature of Radiation and Matter: Deals with the wave-particle duality of radiation and matter.

Photoelectric Effect

• The emission of electrons from a metal surface when light strikes it.
• Einstein's photoelectric equation: KEmax = hν - Φ, where KEmax is the maximum kinetic energy of the emitted electrons, hν is the energy of the incident photon, and Φ is the work function of the metal.

Matter Waves (de Broglie Waves)

• Waves associated with moving particles.

• de Broglie wavelength (λ) = h/p = h/mv, where h is Planck's constant, p is the momentum, m is the mass, and v is the velocity.

• Atoms: Studies the structure and properties of atoms.

Atomic Models

• Thomson's model: Proposed that atoms are uniform spheres of positive charge with electrons embedded in them.
• Rutherford's model: Proposed that atoms have a small, positively charged nucleus surrounded by orbiting electrons.

Bohr's Model

• Electrons revolve around the nucleus in specific orbits without radiating energy.
• Energy levels are quantized.
• Bohr's quantization condition: mvr = n(h/2π), where n is an integer.

Hydrogen Spectrum

• The spectrum of light emitted by hydrogen atoms.

• Lyman series, Balmer series, Paschen series, Brackett series, Pfund series.

• Nuclei: Explores the structure and properties of atomic nuclei.

Nuclear Structure

• Nucleus consists of protons and neutrons (nucleons).
• Atomic number (Z): The number of protons in the nucleus.
• Mass number (A): The total number of protons and neutrons in the nucleus.

Nuclear Binding Energy

• The energy required to separate the nucleons in a nucleus.
• Binding energy per nucleon = (Total binding energy)/A.

Nuclear Reactions

• Reactions involving atomic nuclei.
• Nuclear fission: The splitting of a heavy nucleus into two lighter nuclei.
• Nuclear fusion: The combining of two light nuclei to form a heavier nucleus.

Radioactivity

• The spontaneous emission of particles or energy from unstable nuclei.

• Alpha decay, beta decay, gamma decay.

• Half-life: The time it takes for half of the radioactive nuclei in a sample to decay.

• Semiconductor Electronics: Materials, Devices and Simple Circuits: Covers semiconductors and their applications.

Semiconductors

• Materials with conductivity between conductors and insulators.
• Intrinsic semiconductors: Pure semiconductors, like silicon and germanium.
• Extrinsic semiconductors: Semiconductors doped with impurities.

p-type and n-type Semiconductors

• p-type: Doped with trivalent impurities (e.g., boron), creating holes.
• n-type: Doped with pentavalent impurities (e.g., phosphorus), creating excess electrons.

p-n Junction

• The boundary between p-type and n-type semiconductors.
• Depletion region: A region near the junction with no mobile charge carriers.
• Barrier potential: The potential difference across the depletion region.

Semiconductor Diode

• A device formed by a p-n junction.
• Forward bias: The p-side is connected to the positive terminal, and the n-side is connected to the negative terminal.
• Reverse bias: The p-side is connected to the negative terminal, and the n-side is connected to the positive terminal.

Transistors

• Semiconductor devices used for amplification and switching.
• Bipolar junction transistors (BJTs): n-p-n and p-n-p transistors.
• Field-effect transistors (FETs): JFETs and MOSFETs.

Digital Electronics and Logic Gates

• Logic gates: Electronic circuits that perform logical operations.
• AND gate, OR gate, NOT gate, NAND gate, NOR gate.