Physics Study Summary

This summary covers key concepts and problem types from various topics in Electricity and Magnetism, Semiconductors, and Basic Circuits, as observed in the provided questions.

1. Electric Fields & Charges

• Electric Field Intensity (E):
  • Definition: Force per unit charge (E = F/q).
  • Between parallel plates: E = V/d.
  • From a point charge: E = k|q|/r².
  • Units: Newtons per Coulomb (N/C) or Volts per meter (V/m).
• Electric Flux (Φ): Calculated as Φ = EA cosθ (where E is electric field, A is area, θ is angle between E and area normal).
• Coulomb's Law: Force between two point charges F = k|q₁q₂|/r².
  • Coulomb's constant (k) unit: N·m²/C².
• Electric Dipole: A system with no net charge but produces an electric field.
• Potential Energy (ΔPE) / Work Done: For a charge (q) moving through a potential difference (ΔV): ΔPE = qΔV.
• Charge calculation: Q = I × t (Current × time).
• Electric field lines: Show direction of force on a positive test charge; denser lines mean stronger field.

2. Capacitors

• Parallel Plate Capacitors:
  • Capacitance (C): C = ε₀A/d (ε₀ is permittivity of free space, A is plate area, d is separation).
  • Charge stored (Q): Q = CV.
  • With dielectric/metal sheet: Inserting a dielectric increases capacitance (C_new = κC_old). Inserting a metal sheet of thickness 't' reduces effective distance to (d-t), so C_new = ε₀A/(d-t).
• Series & Parallel Combinations:
  • Series: 1/Ceq = 1/C₁ + 1/C₂ + ...
  • Parallel: Ceq = C₁ + C₂ + ...
• Charging RC Circuits:
  • Maximum charging current (at t=0): Imax = V/R.
  • Charge stored when fully charged: Q = CV.
• Energy Stored (E): E = ½CV² = ½Q²/C = ½QV.

3. Resistors & Circuits

• Ohm's Law: V = IR. Applicable to linear circuits/components.
• Equivalent Resistance (Req):
  • Series: Req = R₁ + R₂ + ...
  • Parallel: 1/Req = 1/R₁ + 1/R₂ + ...
• Resistance and Temperature: Rt = R₀(1 + αΔT) (α is temperature coefficient).
• Total Current in Parallel Resistors: Itotal = V/Req or Itotal = V/R₁ + V/R₂ + ...
• Energy Consumption: E = I²Rt or P × t.
• Potential Difference Measurement: Voltmeter (measures potential difference).
• Conventional Current: Defined as the direction of flow of positive charge.

4. AC Circuits

• RMS Current (Irms): For a sinusoidal voltage, Irms = Vpeak / (√2 × R).
• Peak-to-peak Voltage (Vp-p): Vp-p = 2 × Vpeak = 2√2 × Vrms.
• Power Dissipated (P): P = V²/R = I²R.
• Inductors:
  • Inductive Reactance (XL): XL = 2πfL (f is frequency, L is inductance).
  • Current in Inductor (I): I = V/XL.
• Frequency from Voltage Equation: If v = Vpeak sin(ωt), then angular frequency ω = 2πf, so f = ω/(2π).

5. Semiconductors

• Intrinsic Semiconductors:
  • Current flow due to breakage of crystal bonds.
  • Number of electrons and holes are equal.
  • Band structure is between that of metals and insulators.
• Doping (Extrinsic Semiconductors):
  • P-type: Doping with Group III elements (e.g., Boron in Silicon) creates excess holes.
  • N-type: Doping with Group V elements creates excess electrons in the conduction band.
• PN Junction Diode:
  • Forward bias: +ve terminal to P, -ve terminal to N. Current rises linearly. Depletion region width is reduced.
  • Reverse bias: Current is ideally zero (small leakage current in reality). Depletion region width is increased.
• Resistance and Temperature: For pure semiconductors, resistance *decreases* with increasing temperature (negative temperature coefficient).

6. Magnetism & Induction

• Magnetic Force on Current-Carrying Wire: F = BILsinθ (B is magnetic field, I is current, L is length, θ is angle between I and B).
  • If current is parallel to magnetic field (θ=0° or 180°), force is zero.
• Magnetic Force on Charged Particle: F = qvBsinθ (q is charge, v is velocity).
  • If perpendicular (θ=90°), F = qvB. This force provides centripetal force for circular motion: qvB = mv²/r.
  • Period of circular motion: T = 2πr/v.
• Magnetic Field Lines:
  • Never cross each other.
  • Most concentrated at the poles (strongest field).
  • Go from North pole to South pole outside the magnet, and South to North inside.
• Induced Magnetism: A piece of soft iron attracted to a magnet is an example.
• Electromagnetic Induction: The phenomenon of producing an induced EMF (and hence current) using a changing magnetic field.
  • Accelerating a magnet inside a coil induces current, which reverses direction with the direction of motion.
• Magnetic Field at Coil Center: B = μ₀NI / (2R) (μ₀ is permeability of free space, N is number of turns, I is current, R is radius).
• Magnetic Flux: A measure of the total magnetic field passing through a given area.
• Magnetic Poles: Electric fields do not have magnetic poles; magnetic fields always have associated poles.
• Tesla (T): Unit of magnetic field strength.

7. General Circuit Laws

• Kirchhoff's Current Law (KCL): Applied at a node; states that the algebraic sum of currents entering a node is zero (or sum of currents entering equals sum of currents leaving).

8. Efficiency

• Motor Efficiency: Efficiency = (Output Work / Input Energy) × 100%.
  • Input Energy = Input Power × Time.