94 . Consider the circuit below. (a) What is the initial current through resistor ?2 when the switch is closed? (b) What is the current through resistor ?2 when the capacitor is fully charged, long after the switch is closed? (c) What happens if the switch is opened after it has been closed for some time? (d) If the switch has been closed for a time period long enough for the capacitor to become fully charged, and then the switch is opened, how long before the current through resistor ?1 reaches half of its initial value?
94 . Consider the circuit below. (a) What is the initial current through resistor ?2 when the switch is closed? (b) What is the current through resistor ?2 when the capacitor is fully charged, long after the switch is closed? (c) What happens if the switch is opened after it has been closed for some time? (d) If the switch has been closed for a time period long enough for the capacitor to become fully charged, and then the switch is opened, how long before the current through resistor ?1 reaches half of its initial value?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
94 . Consider the circuit below. (a) What is the initial current through resistor ?2 when the switch is closed? (b) What is the current through resistor ?2 when the capacitor is fully charged, long after the switch is closed? (c) What happens if the switch is opened after it has been closed for some time? (d) If the switch has been closed for a time period long enough for the capacitor to become fully charged, and then the switch is opened, how long before the current through resistor ?1 reaches half of its initial value?
Please show all work using this. (Actual values, equations, and drawings)
![Certainly! Here's a transcription of the handwritten notes and an explanation of the diagram, suitable for an educational website:
---
### Transcription:
**Given:**
\[ R_1 = 10 \times 10^3 \, \Omega \]
\[ R_2 = 300 \, \Omega \]
\[ C_1 = 7 \times 10^{-6} \, F \]
\[ V_i = 29 \, V \]
**Questions:**
a) \( I(R_2, t \rightarrow 0^+) \, ? \)
b) \( I(R_2, t \rightarrow \infty) \, ? \)
c) \( t: I = \frac{I(t=0)}{2} \, ? \)
**Steps:**
1. **At \( t = 0^- \):**
\( Q = 0, \, I_2 = 0 \, A \)
\( \Rightarrow I_1 = I_3 \)
2. **At \( t = 0^+ \):**
\( V_i - (R_1 + R_2) I(t=0) = 0 \)
\[ I_1(t=0) = \frac{V_i}{R_1 + R_2} \]
3. **At \( t = \infty \):**
a) **i) \( I_1 = I_2 + I_3 \)**
b) **ii) \( V_i - I_1 R_2 - I_3 R_2 = 0 \)**
c) **iii) \( \Delta V_c - I_3 R_2 = 0 \Rightarrow \)**
\[ \frac{Q}{C_1} - \frac{dQ/dt}{C_1} - R_1 = 0 \]
\(\Rightarrow q(t) = Q_{\text{max}} e^{-t/R_1C_1}\)
4. **General Equation for Current:**
\[ I(t) = I_0 \cdot e^{-t/R_1C_1} \]
\[ \therefore \frac{I(t)}{I_0} = e^{-t/R_1C_1}, \ln \]
\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F183a4de2-60b8-4988-9fb9-0a70f8d6fd02%2F038c30a4-0a9b-4434-852b-207b895a8233%2Fe3jotd4_processed.png&w=3840&q=75)
Transcribed Image Text:Certainly! Here's a transcription of the handwritten notes and an explanation of the diagram, suitable for an educational website:
---
### Transcription:
**Given:**
\[ R_1 = 10 \times 10^3 \, \Omega \]
\[ R_2 = 300 \, \Omega \]
\[ C_1 = 7 \times 10^{-6} \, F \]
\[ V_i = 29 \, V \]
**Questions:**
a) \( I(R_2, t \rightarrow 0^+) \, ? \)
b) \( I(R_2, t \rightarrow \infty) \, ? \)
c) \( t: I = \frac{I(t=0)}{2} \, ? \)
**Steps:**
1. **At \( t = 0^- \):**
\( Q = 0, \, I_2 = 0 \, A \)
\( \Rightarrow I_1 = I_3 \)
2. **At \( t = 0^+ \):**
\( V_i - (R_1 + R_2) I(t=0) = 0 \)
\[ I_1(t=0) = \frac{V_i}{R_1 + R_2} \]
3. **At \( t = \infty \):**
a) **i) \( I_1 = I_2 + I_3 \)**
b) **ii) \( V_i - I_1 R_2 - I_3 R_2 = 0 \)**
c) **iii) \( \Delta V_c - I_3 R_2 = 0 \Rightarrow \)**
\[ \frac{Q}{C_1} - \frac{dQ/dt}{C_1} - R_1 = 0 \]
\(\Rightarrow q(t) = Q_{\text{max}} e^{-t/R_1C_1}\)
4. **General Equation for Current:**
\[ I(t) = I_0 \cdot e^{-t/R_1C_1} \]
\[ \therefore \frac{I(t)}{I_0} = e^{-t/R_1C_1}, \ln \]
\
Transcribed Image Text:The diagram illustrates an electrical circuit consisting of several components.
1. **Voltage Source (V1):**
- The circuit is powered by a battery providing a voltage of \( V_1 = 24 \text{ V} \).
2. **Resistors:**
- There are two resistors in the circuit:
- \( R_1 = 10 \text{ k}\Omega \)
- \( R_2 = 30 \text{ k}\Omega \)
3. **Capacitor (\( C_1 \)):**
- A capacitor with a capacitance of \( 10 \, \mu\text{F} \) is included in the circuit.
4. **Switch:**
- A switch is present in the circuit, which can be opened or closed to control the flow of current.
5. **Circuit Configuration:**
- The components are arranged in a mixed series-parallel configuration.
- The switch and \( R_1 \) are in series with the voltage source.
- \( R_2 \) is in parallel with the capacitor \( C_1 \).
The circuit can be used to study the behavior of resistors and capacitors in varying configurations, particularly observing the effects of charging and discharging in the capacitor through the resistors when the switch is operated.
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!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON