Practice Problems

Practice Problems#

Problem 1

Plot the following equations:

a) \(v(t) = -2 + 2\cos(360°\cdot 100\ \text{Hz}\cdot t)\ \text{mV}\)

b) \(v(t) = 2\cos(360°\cdot 10\ \text{Hz}\cdot t)\ \text{V}\)

c) \(v(t) = 4\cos(360°\cdot 1\ \text{kHz}\cdot t)\ \text{mV}\)

d) What equation is associated with the graph?

e) What equation is associated with the graph?

Problem 2

If \(v_S(t) = 4 + 8\cos(360°\cdot 10\ \text{kHz}\cdot t)\ \text{V}\), graph \(i_X(t)\) for the signal below.

Problem 3

Find the power consumed by the circuit below given \(V_S = 1.5\ \text{V}\).

Problem 4

Find the average power consumed by the circuit below given:

\(v_S(t) = 2.12\cos(360°\cdot 100\ \text{kHz}\cdot t)\ \text{V}\)

Compare the power consumed by the two circuits (Problems 3 and 4). What can you say about the power consumed?

Problem 5

What is \(\frac{1}{\text{Hz}}\) equivalent to?

a. s   b. 1/s   c. f   d. None of the above

Problem 6

A 9 V battery is connected to a resistor that consumes 7.22 mW of power. Which of the following AC sources would cause the same resistor to consume 7.22 mW of average power?

a. \(7.22\cos(360°\cdot 2\ \text{kHz}\cdot t)\ \text{mV}\)
b. \(9\cos(360°\cdot 2\ \text{kHz}\cdot t)\ \text{V}\)
c. \(7.22\ \text{mV}_{RMS}\)
d. \(9\ \text{V}_{RMS}\)

Problem 7

A B-52 generator produces the signal \(v(t) = 290\cos(360°\cdot 400\ \text{Hz}\cdot t)\ \text{V}\).

a. Graph this signal as a function of time.

b. What is the RMS voltage for the generator above?

Problem 8

The fuse for a 2000-lb general-purpose bomb includes a spinner producing \(v(t) = 15\cos(360°\cdot 2\ \text{kHz}\cdot t)\ \text{mV}\). The arming circuit is modeled as three resistors, as shown below. Graph the current signal coming out of the spinner, \(I_S(t)\).

Problem 9

Which of the two sources below produces more average power?

Problem 10

The circuit below has a current source providing \(i(t) = 11.75\cos(360°\cdot 50\ \text{Hz}\cdot t)\ \text{A}\).

Find \(v_1(t)\).

Problem 11

An AC-powered electric fan, modeled as a 150 Ω resistor, is plugged into a standard 120 VRMS wall outlet. Since the fan requires 90 VRMS to operate, a resistor is added to form a voltage divider.

Given:

  • \(V_S = 120\ \text{V}_{RMS}\)

  • \(R_{fan} = 150\ \Omega\)

Find the resistor value \(R\) required to provide the fan with 90 VRMS.