A Level Physics Derivations

These flashcards cover essential derivations and equations relevant to A Level Physics.

Electrical Power

The expression linking power, current, potential difference, and resistance: P = I²R, P = V²/R.

Resistors in Series

The total resistance of resistors in series is calculated using: RT = R₁ + R₂ + … + Rn.

Resistors in Parallel

The total resistance of resistors in parallel is calculated by: 1/RT = 1/R₁ + 1/R₂ + … + 1/Rn.

Drift Velocity

The expression for calculating drift velocity of charge carriers: I = nAev.

Gravitational Potential Energy

The expression for gravitational potential energy in a uniform field: E_p = mgh.

Kinetic Energy

The expression for kinetic energy: E_k = ½mv².

Elastic Potential Energy

The expression for elastic potential energy stored in a spring: E_e = ½kx².

Energy and Momentum

Kinetic energy in terms of momentum and mass: E_k = p² / (2m).

Power, Force, and Velocity

The expression for power in terms of force and velocity: P = Fv.

‘suvat’ Equations

The equations for an object undergoing uniform acceleration: v = u + at, v² = u² + 2as, s = ut + ½at², s = ½(u + v)t.

Newton’s 2nd Law

The expression relating resultant force to the rate of change of momentum: F = Δp / Δt.

Upthrust

The expression for upthrust on an object submerged in a fluid: U = ρVg.

Springs in Series

The combined stiffness of springs in series: 1/kT = 1/k₁ + 1/k₂ + … + 1/kn.

Springs in Parallel

The combined stiffness of springs in parallel: kT = k₁ + k₂ + … + kn.

Diffraction Grating

The path difference for diffraction is given by: d sin θ = nλ.

Double Slit Fringe Spacing

The expression for fringe spacing from a double slit: λ = ax / D.

Half-life

The expression for the half-life of a radioactive isotope: t_½ = ln2 / λ.

Energy in a Capacitor

Energy stored by a capacitor: E = ½CV², E = ½Q²/C.

Capacitors in Series

The total capacitance of capacitors in series: 1/CT = 1/C₁ + 1/C₂ + … + 1/Cn.

Capacitors in Parallel

The total capacitance of capacitors in parallel: CT = C₁ + C₂ + … + Cn.

Closest Approach

The expression for distance of closest approach for an alpha particle: r = (qQ) / (4πε₀mv²).

Coulomb's Law

The expression for the force between two charged objects: F = k(q₁q₂) / r².

Gravitational Attraction

Newton's law of universal gravitation: F = GMm/r².

Gravitational Field Strength

Gravitational field strength at a distance: g = -GM/r².

Radial Path

The radius of a path for a charged particle in a magnetic field: r = p / (BQ).

Velocity Selector

The expression for the velocity of a particle in a magnetic and electric field: v = E/B.

Centripetal Acceleration

The expression for centripetal acceleration: a_c = v²/r.

Orbital Period and Radius

The relationship between orbital period squared and orbital radius cubed: T² = (4π²/GM) * r³.

Simple Harmonic Motion

For a system undergoing SHM, acceleration: a = -ω²x.

Total Energy of a Satellite

The total energy of a satellite: E_T = -GMm/2R.

Escape Velocity

The expression for escape velocity from a planet: v = √(2GM/r).

Period of a Pendulum

The time period for a pendulum: T = 2π√(l/g).

Period of a Spring-Mass

The time period for a spring-mass system: T = 2π√(m/k).

Ideal Gas Equation

The ideal gas law: PV = nRT.

Kinetic Theory

The kinetic theory formula for an ideal gas: pV = (1/3)Nmc².

The Parsec

1 parsec = 3.1 x 10¹⁶ m.

Specific Charge on an Electron

The expression for the specific charge on an electron: e/m.