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Molecular Chain (MIT, Princeton, Colorado)
Consider a one-dimensional chain consisting of N molecules which exist in two configurations, α, β, with corresponding energies and lengths α and β. The chain is focus to a tensile force f.
a) Write down the partition function ZN for the system.
b) Compute the average length (L) as a function f of and the temperature T.
c) Assume that anda>b. Evaluate the average length (L) in the absence of the tensile force f = 0 as a function of temperature. What are the high-temperature and low-temperature limits and what is the characteristic temperature at which the changeover between the two limits takes place?
d) Estimate the linear response function
Produce a universal argument to show that X>0.
Determine the total energy loss: Two capacitors C 1 = 50 μF and C 2 = 100 μF are connected in parallel across 250 V supply. Determine the total energy loss. Figure
advantages over other theorams
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Calculate the current flow in 30Ω resistor for the circuit in figure using Norton Theorem.
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(a) A second order Sallen and Key Low Pass Active Filter has these component values R 1 =R 2 =15 kΩ, C 1 =C 2 =1 nF and the feedback resistors are R 3 =3.9 kΩ and R 4 =2.3 kΩ
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