Mastering Electronics
Homework 7
Due: Sunday, Oct. 20 2024, at 11:59pm
Problem 1: (15 points)
Consider the sinusoidal voltage
U(t) = 40cos(100πt +60o ) V. (1)
(i) What is the maximum amplitude of the voltage?
(ii) What is the frequency in hertz?
(iii) What is the frequency in radians per second?
(iv) What is the phase angle in radians?
(v) What is the phase angle in degrees?
(vi) What is the period in milliseconds?
(vii) What is the first time after t = 0 that U(t) = −40V ?
(viii) The sinusoidal function is shifted 3/10 ms to the right along the time axis. What is the expression for U(t)?
(ix) What is the minimum number of milliseconds that the function must be shifted to the left if the expression for U(t) is 40sin(100πt) ?
Problem 2: (15 points)
The expressions for the steady-state voltage and current at the terminals of the circuit seen in Fig. 1 are:
vg(t) = 300 cos(5000πt + 78o
) V. (2)
ig(t) = 6 sin(5000πt + 123o
) A. (3)
(i) What is the impedance seen by the source?
(ii) By how many microseconds is the current out of phase with the voltage?
Figure 1: Problem 2
Problem 3: (15 points)
There is no energy stored in the capacitors C1 and C2 at the time the switch is closed in the circuit seen in Fig. 2
(i) Derive the expressions for v1(t) and v2(t) for t ≥ 0
(ii) Use the expressions derived in (a) to find v1(∞) and v2(∞ )
Figure 2: Problem 3
Problem 4: (15 points)
The capacitor in the circuit seen in Fig. 3 has been charged to 300 V. At t = 0 switch 1 closes, causing the capacitor to discharge into the resistive network. Switch 2 closes 200μs after switch 1 closes. Find the magni- tude and direction of the current in the second switch 300μs after switch 1 closes.
Figure 3: Problem 4
Problem 5: (15 points)
The inductor current in the circuit in Fig. 4 is 25 mA at the instant the switch is opened. The inductor will malfunction whenever the magnitude of the inductor current equals or exceeds 5 A. How long (if ever) after the switch is opened does the inductor malfunction?
Figure 4: Problem 5
Problem 6: (15 points)
The energy stored in the capacitor in the circuit shown in Fig. 5 is zero at the instant the switch is closed. The ideal operational amplifier reaches saturation in 15 ms. What is the numerical value of R?
Figure 5: Problem 6
Problem 7: (10 points)
There is no energy stored in the capacitors in the circuit shown in Fig.6 at the instant the two switches close. Assume the op amp is ideal.
(i) Find vo (t) as a function of va, vb,R, and C.
(ii) On the basis of the result obtained in (a), describe in words the opera- tion of the circuit.
(iii) How long will it take to saturate the amplifier if va = 40mV; vb = 15mV ; R = 50kΩ ; C = 10nF ; and VCC = 6V ?
Figure 6: Problem 7