Consider a series RC circuit as in the figure below for which R = 6.70 M2, C = 4.70 μF, and = 25.5 V. + E S R (a) Find the time constant of the circuit. 31.49 (b) Find the maximum charge on the capacitor after the switch is thrown closed. 1.1985e-4 X What is the current in the circuit when the capacitor has reached its maximum charge? μC (c) Find the current in the resistor 10.0 s after the switch is closed. MA
Consider a series RC circuit as in the figure below for which R = 6.70 M2, C = 4.70 μF, and = 25.5 V. + E S R (a) Find the time constant of the circuit. 31.49 (b) Find the maximum charge on the capacitor after the switch is thrown closed. 1.1985e-4 X What is the current in the circuit when the capacitor has reached its maximum charge? μC (c) Find the current in the resistor 10.0 s after the switch is closed. MA
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
100%
![**RC Circuit Analysis**
Consider a series RC circuit as shown in the diagram. The values for the components of the circuit are as follows:
- Resistance (R) = 6.70 MΩ
- Capacitance (C) = 4.70 μF
- Electromotive Force (ℰ) = 25.5 V
**Tasks:**
(a) **Find the time constant of the circuit.**
The time constant (τ) is calculated using the formula:
\[ \tau = R \times C \]
The time constant is:
\[ \boxed{31.49} \, \text{s} \]
(b) **Find the maximum charge on the capacitor after the switch is thrown closed.**
\[ Q_{\text{max}} = C \times \mathcal{E} \]
The attempted calculation shows an incorrect value:
\[ 1.1985 \times 10^{-4} \, \text{μC (incorrect)} \]
The statement, "What is the current in the circuit when the capacitor has reached its maximum charge?" is given, which indicates a follow-up question on the same topic.
(c) **Find the current in the resistor 10.0 seconds after the switch is closed.**
\[ I(t) = \frac{V}{R} e^{-t/\tau} \]
Fill in the current value:
\[ \boxed{ \, \text{µA} } \]
**Diagram Details:**
- The circuit diagram includes a resistor (R) and a capacitor (C) connected in series, with a switch (S) that can be closed to complete the circuit.
- The power source provides a potential difference represented by ℰ, with the positive terminal connected to the capacitor.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75efe16f-f4aa-4987-9727-1ee0c2946a7c%2Fa587ff14-66c2-449d-b748-35eaf14afbd7%2Fsip20f9_processed.png&w=3840&q=75)
Transcribed Image Text:**RC Circuit Analysis**
Consider a series RC circuit as shown in the diagram. The values for the components of the circuit are as follows:
- Resistance (R) = 6.70 MΩ
- Capacitance (C) = 4.70 μF
- Electromotive Force (ℰ) = 25.5 V
**Tasks:**
(a) **Find the time constant of the circuit.**
The time constant (τ) is calculated using the formula:
\[ \tau = R \times C \]
The time constant is:
\[ \boxed{31.49} \, \text{s} \]
(b) **Find the maximum charge on the capacitor after the switch is thrown closed.**
\[ Q_{\text{max}} = C \times \mathcal{E} \]
The attempted calculation shows an incorrect value:
\[ 1.1985 \times 10^{-4} \, \text{μC (incorrect)} \]
The statement, "What is the current in the circuit when the capacitor has reached its maximum charge?" is given, which indicates a follow-up question on the same topic.
(c) **Find the current in the resistor 10.0 seconds after the switch is closed.**
\[ I(t) = \frac{V}{R} e^{-t/\tau} \]
Fill in the current value:
\[ \boxed{ \, \text{µA} } \]
**Diagram Details:**
- The circuit diagram includes a resistor (R) and a capacitor (C) connected in series, with a switch (S) that can be closed to complete the circuit.
- The power source provides a potential difference represented by ℰ, with the positive terminal connected to the capacitor.
Expert Solution
Step 1
Given,
R = 6.70 MΩ = 6.70 x 106 Ω
C = 4.70 μF = 4.70 x 10-6 F
ε = 25.5 V
Step by step
Solved in 2 steps
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