6.2.3: Problems

Exercise \(\PageIndex{1}\): Power of light bulbs (with switches)

Assume an ideal power supply. The graph shows the voltage across the power supply \(\color{red}{\text{(red)}}\) and current (\(\times 100\)) from the power supply \(\color{blue}{\text{(blue)}}\) as a function of time (voltage is given in volts, current is given in hundredths of amperes, and time is given in seconds). A measurement of a current of \(50\) on the graph would actually be a current of \(0.5\text{ A}\). Find the power rating of each of the bulbs \(A,\: B,\: C,\) and \(D\). Restart.

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian and Anne J. Cox

Exercise \(\PageIndex{2}\): Transformer

A transformer is connected to an outlet. The graph shows the input voltage (voltage across the primary) and output voltage (voltage across the secondary and resistor) as a function of time. You can read the resistor value by moving the mouse over the resistor. Restart.

1. If the primary has \(400\) windings, how many windings does the secondary have?
2. What is the rms current delivered to the primary?
3. How much power is delivered to the resistive load?

Problem authored by Anne J. Cox.
Script authored by Morten Brydensholt and modified by Anne J. Cox.

Exercise \(\PageIndex{3}\): Power and resistive loads

Assume an ideal power supply. The graph shows the voltage across the source \(\color{red}{\text{(red)}}\) and the current through the circuit \(\color{blue}{\text{(blue)}}\) as functions of time (voltage is given in volts, current is given in milliamperes [\(10^{-3}\) amperes], and time is given in seconds). Restart. For each circuit,

What is the rms voltage? What is the rms current? What is the value of the unknown resistor? What is the average power dissipated?

1. Circuit I
2. Circuit II
3. Circuit III

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian and Anne J. Cox.

Exercise \(\PageIndex{4}\): Identify the unknown element

Identify the following unknown circuit elements (resistor, capacitor or inductor) and match the frequency response graphs (Graphs A--C) to the current and voltage vs. time graphs shown for the circuits below. Explain your answers. Restart.

1. Circuit I
2. Circuit II
3. Circuit III

Problem authored by Morten Brydensholt and Wolfgang Christian.

Exercise \(\PageIndex{5}\): Determine value of component

Determine the value of the circuit elements (voltage is given in volts, current is given in amperes, and time is given in seconds). Restart.

1. Capacitor
2. Inductor

Problem authored by Mario Belloni and Wolfgang Christian.

Exercise \(\PageIndex{6}\): RC series circuit

Assume an ideal power supply. The voltage of the source is \(\color{red}{\text{red}}\), the voltage across the resistor is \(\color{blue}{\text{blue}}\), and the voltage across the capacitor is \(\color{green}{\text{green}}\). Identify the correct graph for the RC series circuits shown (voltage is given in volts and time is given in seconds). Restart.

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian and Anne J. Cox.

Exercise \(\PageIndex{7}\): RL Series Circuit

Assume an ideal power supply. The voltage of the source is the \(\color{red}{\text{red}}\), the voltage across the resistor is \(\color{blue}{\text{blue}}\), and the voltage across the inductor is \(\color{green}{\text{green}}\). Identify the correct graph for the RL series circuits shown (voltage is given in volts and time is given in seconds). Restart.

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian and Anne J. Cox.

Exercise \(\PageIndex{8}\): RC oscillations

Assume ideal circuit components (voltage across the capacitor \(\color{blue}{\text{[blue]}}\) is given in volts, current \(\color{red}{\text{[red]}}\) is given in milliamperes, and time is given in seconds). A capacitor is charged and connected to an inductor. Watch what happens to the voltage across the capacitor and to the current. Restart.

1. What is the value of the inductor?
2. What is the average power dissipated? Why?

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian and Anne J. Cox.

Exercise \(\PageIndex{9}\): Find power with \(R\) from \(V\) and \(I\) graphs

Assume an ideal power supply. The voltage of the source as a function of time is the \(\color{red}{\text{red}}\) plot on the graph, and the current from the source is \(\text{black}\) (voltage is given in volts, current is given in milliamperes \([\text{mA }= 10^{-3}\text{ A}]\), and time is given in seconds). Restart. What is the power dissipated in each circuit?

1. Circuit I: RC Circuit
2. Circuit II: RL Circuit
3. Circuit III: RLC Circuit

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian and Anne J. Cox.

Exercise \(\PageIndex{10}\): Speaker system design

Assume an ideal power supply. The voltage of the source is the \(\color{red}{\text{red}}\) plot on the graph. Restart.

1. Which plot shows the voltage across resistor \(A\)?
2. Which is the voltage across resistor \(B\)?

This is a basic design of a loudspeaker system in which the resistors represent speakers: a tweeter and a woofer. The woofer, a large speaker, wants low-frequency signals (and generates low-pitched sound), while the tweeter, the small-diameter speaker, should get high-frequency signals (to generate high-pitched sound).

3. Which resistor represents the tweeter and which represents the woofer? Explain.

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian and Anne J. Cox.

Exercise \(\PageIndex{11}\): Determine value of capacitance and power in RC circuit

Assume an ideal power supply. The graph shows the voltage across the source \(\color{red}{\text{(red)}}\) and the current \(\text{(black)}\) through the circuit as a function of time, as well as the voltage across the resistor \(\color{blue}{\text{(blue)}}\) and the voltage across the capacitor \(\color{green}{\text{(green)}}\) (voltage is given in volts, current is given in milliamperes \([\text{mA }= 10^{-3}\text{ A}]\), and time is given in seconds). Restart.

1. What is the value of the unknown capacitor?
2. What is the average power dissipated when the reactance of the capacitor equals the resistance of the resistor?

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian and Anne J. Cox.

Exercise \(\PageIndex{12}\): Determine value of inductor and power in RL circuit

Assume an ideal power supply. The graph shows the voltage across the source \(\color{red}{\text{(red)}}\) and the current \(\text{(black)}\) through the circuit as a function of time, as well as the voltage across the resistor \(\color{blue}{\text{(blue)}}\) and the voltage across the inductor \(\color{green}{\text{(green)}}\) (voltage is given in volts, current is given in milliamperes [\(\text{mA }= 10^{-3}\text{ A}\)], and time is given in seconds). Restart.

1. What is the value of the unknown inductor?
2. What is the average power dissipated when the reactance of the inductor equals the resistance of the resistor?

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian and Anne J. Cox.

Exercise \(\PageIndex{13}\): Rank resistors in switched RLC circuits

Assume an ideal power supply. Rank the resistors in the three switched RLC circuits (you will need to open the switches and start the graph by clicking on the "play" button). The graph shows the voltage across the capacitor as a function of time \(\color{red}{\text{(red)}}\), the voltage across the inductor as a function of time \(\color{blue}{\text{(blue)}}\), and the voltage across the resistor as a function of time \(\color{green}{\text{(green)}}\) (voltage is given in volts and time is given in seconds). Restart.

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian and Anne J. Cox.

Exercise \(\PageIndex{14}\): Resonance curve

The voltage vs. time graph shows the voltages across circuit elements in this circuit. You can vary the frequency of the source voltage (voltage is given in volts, current is given in amperes, time is given in seconds, and frequency is given in hertz). Restart.

1. What is the resonant frequency of this circuit?
2. Which graph describes the frequency response of this circuit? Explain.

Problem authored by Morten Brydensholt and Anne J. Cox.

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