Adiabatic Vcm Figure 1: P-V curve for a Hypothetical Heat Engin... | Filo (2024)

Question asked by Filo student

A battery of internal resistance 4Ω is connected to the network of resistance as shown. In order to give the maximum power to the network, the value of R should be ____ Ω −

In a series LCR circuit, the frequencies at which the current amplitude is 2​1​ times the current amplitude at resonance are f1​ and f2​(>f1​). Find the frequency bandwidth of resonance which is defined as Δf=f2​−f1​. Express your answer in terms of R and L. Assume that resonance frequency f0​≫Δf

Save Progress Submit Ans Need Help m'/m = Find the ratio of the ion masses, m/m. 1 point SerPSE1028.2.OP.010 An ion with a mass m and a magnitude of charge of Ie is initially at rest when it is accelerated by a potential difference of ma Nen has a magnitude of charge of 3e and is accelerated by the potential difference and the magnetic field.

The Dirac equation was derived in class in its classical form as:ihcγ^0ψ = -iha0ψ + 3mcψwhere the Dirac representation of the coefficients above is given by:γ^0 = [1 0 0 0]γ^1 = [0 0 0 1]γ^2 = [0 0 1 0]γ^3 = [0 -1 0 0]The Feynman slash notation is defined as:γ̸ = γ^με_μwhere ε is any covariant 4-vector.i) Write γ̸ explicitly as a 4x4 matrix, using the standard Dirac representation.γ̸ = γ^με_μ = γ^0ε_0 + γ^1ε_1 + γ^2ε_2 + γ^3ε_3 = [1 0 0 0][ε_0] + [0 0 0 1][ε_1] + [0 0 1 0][ε_2] + [0 -1 0 0][ε_3] = [ε_0 0 0 0] + [0 0 0 ε_1] + [0 0 ε_2 0] + [0 -ε_3 0 0]ii) Show that γ̸^2 = 2abL4, where both a and b are any 4-vectors.γ̸^2 = γ^μγ^νε_με_ν = (γ^0γ^0 + γ^1γ^1 + γ^2γ^2 + γ^3γ^3)(ε_0ε_0 + ε_1ε_1 + ε_2ε_2 + ε_3ε_3) = (1*1 + 0*0 + 0*0 + 0*0)(ε_0ε_0 + ε_1ε_1 + ε_2ε_2 + ε_3ε_3) + (0*0 + 0*0 + 0*0 + 1*1)(ε_0ε_0 + ε_1ε_1 + ε_2ε_2 + ε_3ε_3) + (0*0 + 0*0 + 1*1 + 0*0)(ε_0ε_0 + ε_1ε_1 + ε_2ε_2 + ε_3ε_3) + (0*0 + -1*-1 + 0*0 + 0*0)(ε_0ε_0 + ε_1ε_1 + ε_2ε_2 + ε_3ε_3) = (ε_0ε_0 + ε_1ε_1 + ε_2ε_2 + ε_3ε_3) + (ε_0ε_0 + ε_1ε_1 + ε_2ε_2 + ε_3ε_3) + (ε_0ε_0 + ε_1ε_1 + ε_2ε_2 + ε_3ε_3) + (ε_0ε_0 + ε_1ε_1 + ε_2ε_2 + ε_3ε_3) = 2(ε_0ε_0 + ε_1ε_1 + ε_2ε_2 + ε_3ε_3) = 2abL4iii) Simplify the expression Y into a form that has no gamma matrices.