Question

Circuits

(g) Immediately after the switch is closed at t = Os, find the current in the capacitor. (7)

(b) When the switch is open for t < Os, what is the voltage across the capacitor. (6)

(c) When the switch is open for t < Os, find the charge and energy stored in the capacitor. (6)

(d) Immediately after the switch is closed at t = Os, find the voltage across the capacitor. (4)

(k) se the Norton model in figure 2 with the step response of a RC circuit to write the voltage across the capacitor in the form

Find Is, R, Vo and t. (10)

v_{c}(t)=I_{s} R+\left(V_{0}-I_{s} R\right) e^{-t / \tau}

(a) When the switch is open for t < Os, find the currents in the resistors, R1 and R2. (6)

(n) Find the time when the current is down to 50% of the peak value in part (m) (8)

(j) After the switch is closed, find the Norton equivalent current (Is) and resistance (R) acrossthe terminals of the capacitor as shown in figure 2. Use source transformation to find theNorton circuit. (8)

(m)Find the peak current through the capacitor. At what time does the peak current occur.Note you don't have to find the derivative in this case. (7)

(f) Immediately after the switch is closed at t = Os, find the voltage and current in resistor R1.

(i) Long after the switch is closed, what is the energy stored in the capacitor. (5)

(e) Immediately after the switch is closed at t =Os, find the current in resistor R2. (6)

(h) Long after the switch is closed, what are the currents in the resistors, R1 and R2. (6)

Figure 1 shows a circuit consisting of two resistors, a capacitor and a voltage source. The switch is left open for t < Os. At t = Os, the switch is closed. The following questions apply to currents and voltages in this circuit, when the switch goes from being open to being closed. Note that the capacitor looks like an open in the steady state, and the voltage across the capacitor cannot change instantaneously.

(1) Using the relationship between capacitor voltage and current, find an expression for the current through the capacitor in terms of Is, R, Voand z. (8)

(0) If the value of resistor, R2, is changed such that the voltage across the capacitor when t→00 is one half the voltage across the capacitor for t<0, find the new value of R2. (7)  Verified

### Question 52583  Circuits

Problem 3 For the following circuit, use nodal analysis to write the FOUR equations in standard form. DO NOT SOLVE. You must identify any quasi-supernodes, supernodes, auxiliary equations, and remove dependent variables. Your final equations may only have V₁, V2, V3 and/or V4 as unknowns. Put your final equations in standard form in the box provided.

### Question 52582  Circuits

Problem 2 For the following circuit, write the FOUR mesh equations in standard form. DO NOT SOLVE. You must identify any super meshes, auxiliary equations, and re-move all dependent variables. Your equations may only have 11,12,13 and/or 14 as unknowns. Put your final equations in standard form in the box provided.

### Question 52581  Circuits

Problem 1.1 Determine Reg in Ohms at the (a,b) terminals for the following circuit. Round your answer to the nearest single digit decimal place (tenths).
Problem 1.2 Determine the voltage V, in Volts for the following circuit. Round your answer to the nearest single digit decimal place (tenths).
Problem 1.3 Determine the current I, in Amps for the following circuit. Round your answer to the nearest single digit decimal place (tenths).
Problem 1.4 Determine the power, P3n, delivered to the 302 resistor in Watts for the following circuit.Round your answer to the nearest single digit decimal place (tenths).

### Question 45529  Circuits

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

### Question 45528  Circuits

\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.

### Question 45527  Circuits

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)?

### Question 45526  Circuits

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?

### Question 45525  Circuits

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?

### Question 45524  Circuits

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

### Question 45523  Circuits

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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