Boston University EK307 – Fall 2017

Fall 2017 EK307-A( ) Problem Set 7

Name: ____________________, BU I.D.: __________________

Scores: Q(1) _____, Q(2) _____, Q(3) _____, Q(4) _____, Q(5) _____, Q(6) _____, Q(7) _____, Q(8) _____, Q(9) _____, Q(10) _____ Grader (initial) ___________, Total: __________________

Boston University EK307 – Fall 2017

Problem Set 7 For all homework throughout the semester you must do the following: 1. State the nature of the problem and your strategy for solving it. 2. Execute your strategy noting key steps. 3. Write legibly and in a logical order. Label any new variables you introduce in your circuit diagram. Problem 1. A 4-mF capacitor has the terminal voltage

If the capacitor has an initial current of 2 A, find: (a) the constants A and B, (b) the energy stored in the capacitor at t = 0,

(c) the capacitor current for t > 0. Problem 2. Find the voltage across the capacitors in the circuit below under dc conditions.

Problem 3. Determine the equivalent capacitance for the circuit below.

Problem 4. Assuming that the capacitors are initially uncharged at t = 0, find vo(t) in the circuit for t > 0. Give the mathematical form for vo(t) and sketch it.

Problem 5. The voltage across a 2-H inductor is 20(1 − e−2t) V for all times t in seconds. If the initial current through the inductor is 0.3 A, find the current and the energy stored in the

Boston University EK307 – Fall 2017

inductor at t = 1 s. Problem 6. Find vC, iL, and the energy stored in the capacitor and inductor in the circuit below under dc conditions.

Problem 7. An op amp integrator has R = 50 kΩ and C = 0.04 μF. If the input voltage is vi = 10 sin 50t mV, obtain the output voltage. Assume that at t equal to zero, the output is equal to zero. Problem 8. Show how you would use a single op amp to generate

If the integrating capacitor is C = 5 μF, obtain the other component values. Problem 9. The triangular waveform below (left) is applied to the input of the op amp differentiator shown below right. Plot the output and indicate values and units on the x and y axes of your plot.

Problem 10. In the circuit shown below

(a)  Find the values of R and C (b)  Find the time constant τ.