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Plate Resistance.

Plate Resistance: Plate resistance is the ratio of a small change in voltage to the corresponding change in current. Formula : Plate resistance = ΔV / ΔI At Saturation Current: In the saturation region, the diode current remains almost constant even when the applied voltage changes. Therefore, ΔI ≈ 0. Hence, Plate resistance → ∞ (ideally infinite) Important : At saturation current, the plate resistance of a diode is ideally infinite.

Plasma frequency.

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Plasma frequency is the natural frequency at which electrons in a plasma oscillate collectively about their equilibrium positions. where, ● n = Electron number density ● e = Charge of an electron ● mₑ = Mass of an electron ● ε₀ = Permittivity of free space Plasma frequency increases with the square root of electron number density.

prove that trace of a commutator is zero.

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What is partition function ?

The partition function is a fundamental quantity in statistical mechanics that describes how a system is distributed among its possible energy states. For a system in thermal equilibrium: Z = Σ e⁻ᴱⁱ/ᵏᴮᵀ where Eᵢ is the energy of the ith state, kB is the Boltzmann constant, and T is the absolute temperature. The partition function is useful because many thermodynamic quantities, such as internal energy, entropy, and Helmholtz free energy, can be calculated from it.

Integration of e^-x2 from −infinity to +infinity | Gaussian Integral

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Integration 0 to infinity sinx/x

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Proof:-

What is Brewster’s Law?

Brewster’s Law states that when unpolarized light is incident on a transparent surface at the polarizing angle i_B, the reflected and refracted rays are perpendicular to each other.       tan i_B=μ where i_B is the Brewster angle and μ is the refractive index of the medium. Key point: At Brewster angle, the reflected light is completely plane polarized.