Solved: Use the circuit shown below to answer the following questions. The swi

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use the circuit shown below to answer the following questions the swit

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Use the circuit shown below to answer the following questions. The switch shown in the figure below has been open for a very long time, at t=0s, the switch closes. The control current for the CCVS is I(2R) which is the current flowing the 2R resistor, towards ground. The value for CCVS is r I(2R), where r is a trans resistance.

Given VAV ,R, and r, all answers should be in terms of only the known constants: Va , V.B'R, r,B' and any constants, numbers. No other solutions will be accepted, provide all answers in theA' simplest form, simplify.

a) [5pts] Use equivalent circuits to derive an expression for the voltage across the capacitor just before the switch closes.

c) [5pts] After the switch closes, and t → o, derive an expression for the voltage across the capacitor in terms of the knowns.

b) [5pts] Using equivalent circuits, derive an expression for the time constant of the circuit in terms of the knowns for t > 0s.

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Question 45529

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11) From your answer in (10), does the 4V 'DC' or steady state voltage impact the value of the displacement current, Ic.

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\text { 10) Assuming } I_{C}=C \frac{d V_{C}}{d t} \text {, find the displacement current for } V_{C}=e^{-\omega t}+4 V \text { and } V_{C}=
sin(wt) + 4 V.

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9) Based on your answer in (7), can you apply an arbitrarily large field or voltage across a dielectric? What is the name for this limitation and what is its value for Air and Glass (SiO2)?

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8) Remembering quantum tunneling from Chapter 3, what is happening to the probability of a tunneling event as the "thickness" of the barrier representing the dielectric decreases?

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7) What happens to the relative "thickness", or distance an electron must travel in a straight line across the dielectric, as you increase the voltage?

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6) Redraw the diagram in (5) with a small positive voltage on the right-hand side (no voltage or OVon the left-hand side).

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5) Draw the energy band diagram of a capacitor made of two aluminum plates with a glass dielectric. The capacitor should have zero applied voltage.

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\text { Given } C=\frac{\varepsilon A}{d}=\frac{q}{v} \text { and the units of } \varepsilon \text { are } F / m \text {, determine the equivalent units of the Farad (I.E. in }
terms of other available units).

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3) What is the result of increasing thickness of a dielectric (increasing d in the capacitor equation)while keeping the amount of charge on each plate the same? Think in terms of the capacitance and the voltage measured across the capacitor.

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2) Define the displacement current. Are charges physically flowing through the dielectric?