**Problem Statement:**Now suppose we replace the 5 volt source in our circuit with the square wave of magnitude 5 volts (i.e. 10 volts peak-to-peak). What frequency should we make it so that we observe the capacitor charge up to +5 volts for 7 time-constants, and then charge down to -5 volts for 7 time-constants?**Explanation:**This problem involves calculating the frequency of a square wave signal applied to a circuit, ensuring that the capacitor within the circuit follows specified charging and discharging patterns over defined time constants. - **Square Wave Characteristics:** - **Magnitude:** 5 volts (peak value) - **Peak-to-Peak Voltage:** 10 volts- **Time-Constants:** - Charging and discharging of the capacitor should each last for 7 time-constants. To find the required frequency of the square wave, one must consider the time period necessary for the capacitor to charge and discharge as specified, combining these durations to form the period of the desired square wave signal. **Problem 2:****Given:**- A circuit with a voltage source \( V_{in}(t) = 5V \).- Components include a resistor \( R \), an inductor \( L \), and a capacitor \( C \).- The current through the inductor is denoted as \( i_L(t) \).- The voltage across the capacitor is denoted as \( V_C(t) \).**Tasks:****a. Verification:**Verify that the differential equation for \( v_C(t) \) is:\[v_C'' + \frac{R}{L}v_C' + \frac{1}{LC}v_C = \frac{5}{LC}\]**b. Calculation:**Find \( v_C(t) \) given:- \( R = 330 \Omega \)- \( L = 100 \text{ mH} \)- \( C = 0.1 \mu F \)**Diagram Explanation:**The diagram depicts a series RLC circuit. The components are connected in the following order:- An AC voltage source \( V_{in}(t) = 5V \).- A resistor \( R \).- An inductor \( L \).- A capacitor \( C \), with the voltage across it denoted as \( V_C(t) \).The objective is to analyze the circuit's behavior and validate the given differential equation for the capacitor voltage, followed by calculating \( V_C(t) \) using the given component values.

c. Consider the square-wave input voltage. The capacitor charges when the voltage is positive, that is, for the positive half cycle and discharges when the voltage is negative, that is, for the negative half cycle. The charging time is 7 time constants and the discharging time is also 7 time constants. Thus, the total time period of the capacitor voltage is 7+7, that is, 14 time constants. The period of the capacitor voltage is same as that of that of the input voltage. The time constant of the RC circuit is equal to RC.Determining the period of the square wave. T=7RC+7RC =14RCDetermining the frequency of the square wave.f=1Tf=114RCIf R=1kΩ and C=0.1μFf=114RC=114×103×0.1×10-6f=714.3 Hz

Engineering

Electrical Engineering

c. Now suppose we replace the 5 volt source in our circuit with the squarewave of magnitude 5 volts (i.e. 10 volts peak-to-peak). What frequency should we make it so that we observe the capacitor charge up to +5 volts for 7 time-constants, and then charge down to -5 volts for 7 time-constants?

c. Now suppose we replace the 5 volt source in our circuit with the squarewave of magnitude 5 volts (i.e. 10 volts peak-to-peak). What frequency should we make it so that we observe the capacitor charge up to +5 volts for 7 time-constants, and then charge down to -5 volts for 7 time-constants?

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Related questions

Q: 5. What value of the current when a capacitor of 10uF connected to a 110V a.c. 50 Hz power supply?…

A: Given, Capacitance, C=10 μF. Supply voltage, V=110 V. Frequency, f = 50 Hz.

Q: Problem: 2.6.12.

Q: Describe how a capacitor can be used in a DC circuit to store charge /turn on a lightbulb without…

A: We can use capacitor to store charge and light the bulb as

Q: a. Quantify how the resistors and the capacitor influence the outputvoltage of the circuit, Vout.…

Q: Design a circuit to limit a 20 V rms sinusoidal voltage to a maximum positive amplitude of 10 V and…

A: Clipper Circuits:- A clipper circuit is used to clip the input voltage at a fixed higher and lower…

Q: Suppose we have a 10-Hz sinusoidal voltage source, vin(t). Draw the diagram of a circuit that clamps…

A: Drawing a circuit that clamps the positive peaks to - 4 V

Q: The question is attached to jpeg picture of the circuit:

A: Please find the below answer in which I have explained clearly by step by step. So, please give good…

Q: Veut Vin Vu 1kN 1kN c) c) Vin Veut Vin

A: *Multiple Sub- parts* # as per our guidelines we are supposed to answer ?️only first 3️⃣…

Q: a. Quantify how the resistors and the capacitor influence the output voltage of the circuit, Vout.…

A: a) The circuit is given as Case 1: Vout=+VCCVoltage at terminal x will beVx=R2R×(+VCC)Vx=VCC2=…

Q: Q6. Figure Q6 shows a modulated waveform v(t) in microvolts as a function of time t in nanoseconds.…

A: A message signal is transferred from the sender to the receiver end. The signal is transmitted…

Q: A capacitive pressure sensor has its nominal capacitance, Cs, as 1.5 pF. It is interfaced with an…

Q: Draw a diagram of a 60 Hz AC voltage waveform that is being altered by a 3rd (2)harmonic where the…

A: Step 1:• If the frequency of the waveform of the main signal is fo=60Hz. Then the frequency of the…

Q: what FR4 rogers in detail

A: FR4 and Rogers are two different materials used in printed circuit boards (PCBs). FR4 is a common…

Q: Q6. Explain why an a.c capacitor that is working in an a.c circuit will get hot, whereas a d.c…

A: AC Capacitor in an AC CircuitReactive Power: Each cycle of AC voltage causes the capacitor to absorb…

Question

**Problem Statement:**

Now suppose we replace the 5 volt source in our circuit with the square wave of magnitude 5 volts (i.e. 10 volts peak-to-peak). What frequency should we make it so that we observe the capacitor charge up to +5 volts for 7 time-constants, and then charge down to -5 volts for 7 time-constants?

**Explanation:**

This problem involves calculating the frequency of a square wave signal applied to a circuit, ensuring that the capacitor within the circuit follows specified charging and discharging patterns over defined time constants.

- **Square Wave Characteristics:**
- **Magnitude:** 5 volts (peak value)
- **Peak-to-Peak Voltage:** 10 volts

- **Time-Constants:**
- Charging and discharging of the capacitor should each last for 7 time-constants.

To find the required frequency of the square wave, one must consider the time period necessary for the capacitor to charge and discharge as specified, combining these durations to form the period of the desired square wave signal.

**Problem 2:**

**Given:**
- A circuit with a voltage source \( V_{in}(t) = 5V \).
- Components include a resistor \( R \), an inductor \( L \), and a capacitor \( C \).
- The current through the inductor is denoted as \( i_L(t) \).
- The voltage across the capacitor is denoted as \( V_C(t) \).

**Tasks:**

**a. Verification:**
Verify that the differential equation for \( v_C(t) \) is:

\[
v_C'' + \frac{R}{L}v_C' + \frac{1}{LC}v_C = \frac{5}{LC}
\]

**b. Calculation:**
Find \( v_C(t) \) given:
- \( R = 330 \Omega \)
- \( L = 100 \text{ mH} \)
- \( C = 0.1 \mu F \)

**Diagram Explanation:**
The diagram depicts a series RLC circuit. The components are connected in the following order:
- An AC voltage source \( V_{in}(t) = 5V \).
- A resistor \( R \).
- An inductor \( L \).
- A capacitor \( C \), with the voltage across it denoted as \( V_C(t) \).

The objective is to analyze the circuit's behavior and validate the given differential equation for the capacitor voltage, followed by calculating \( V_C(t) \) using the given component values.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions

double clipper circuit Zener diodes 1N4733A has a voltage of 5.1 V and 1N4735A has a voltage of 6.2 V with a resistor R=300ohms has been used. you may like to increase the input to a 12 VRMS AC source in order to see the clipping at 7volt. Please, Do the theoretical calculations and plot the expected waveforms by hand. ( I have its multisim design and only needs theoretical calculation and hand drawn graph of it to compare to its data that I have collected from multism.) Thanks
Do we need to take into account the internal resistance of the voltmeter when discharging the capacitor? Why or why not?
An inductor of 150hms and resistance of 10 Ohms are connected in series to a 230V, 50 Hz ac supply. Determine the active and reactive power and power factor in the circuit.
Example-3 Thank you
Please do D, E, and F