Homework Help is Here – Start Your Trial Now!
Science
Physics
An R=131k resistor and a C=26μF capacitor are connected in series with a open switch. The capacitor is initially fully charged to an initial potential of V₁ = 21V. The switch is closed at t = 0. Determine the current in the circuit when the charge on the capacitor is 1/7 of its maximum value (in μA).

An R=131k resistor and a C=26μF capacitor are connected in series with a open switch. The capacitor is initially fully charged to an initial potential of V₁ = 21V. The switch is closed at t = 0. Determine the current in the circuit when the charge on the capacitor is 1/7 of its maximum value (in μA).

College Physics
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)...
See similar textbooks
icon
Related questions
Question
An R=131k52 resistor and a C =26. capacitor are connected in series with a open switch. The capacitor is initially fully charged to an initial potential of Vo =21V. The switch is closed att = 0. Determine the current in the circuit when the charge on the capacitor is 1/7 of its maximum value Could you please look at correct answer and show all work
**Transcription and Explanation for Educational Website** --- **Problem Statement:** An \( R = 131 \, k\Omega \) resistor and a \( C = 26 \, \mu F \) capacitor are connected in series with an open switch. The capacitor is initially fully charged to an initial potential of \( V_0 = 21 \, V \). The switch is closed at \( t = 0 \). Determine the current in the circuit when the charge on the capacitor is \( \frac{1}{7} \) of its maximum value (in \(\mu A\)). **Your Answer:** 17.07 **Correct Answer:** 22.9008 (margin of error +/- 1%) --- **Explanation:** This problem involves analyzing an RC (resistor-capacitor) circuit where the capacitor is initially charged, and you need to determine the current when the charge drops to a specific fraction of its initial value. **Key Concepts:** 1. **RC Circuit Dynamics:** - When the switch is closed, the circuit begins to discharge. - The current (\( I(t) \)) and the charge (\( Q(t) \)) on the capacitor change over time based on exponential decay. 2. **Capacitor Charge Equation:** - \( Q(t) = Q_0 \cdot e^{-t/(RC)} \) where \( Q_0 = C \cdot V_0 \). 3. **Current Equation:** - \( I(t) = \frac{V_0}{R} \cdot e^{-t/(RC)} \). 4. **Given Condition:** - The problem states \( Q(t) = \frac{1}{7}Q_0 \). - Use this condition to find \( t \) and subsequently find \( I(t) \). 5. **Steps to Solve:** - Compute \( Q_0 = C \cdot V_0 \). - Substitute \( Q(t) = \frac{1}{7}Q_0 \) into \( Q(t) = Q_0 \cdot e^{-t/(RC)} \) to solve for \( t \). - Substitute \( t \) back into \( I(t) = \frac{V_0}{R} \cdot e^{-t/(RC)} \) to find the current at that time. This exercise
Transcribed Image Text:**Transcription and Explanation for Educational Website** --- **Problem Statement:** An \( R = 131 \, k\Omega \) resistor and a \( C = 26 \, \mu F \) capacitor are connected in series with an open switch. The capacitor is initially fully charged to an initial potential of \( V_0 = 21 \, V \). The switch is closed at \( t = 0 \). Determine the current in the circuit when the charge on the capacitor is \( \frac{1}{7} \) of its maximum value (in \(\mu A\)). **Your Answer:** 17.07 **Correct Answer:** 22.9008 (margin of error +/- 1%) --- **Explanation:** This problem involves analyzing an RC (resistor-capacitor) circuit where the capacitor is initially charged, and you need to determine the current when the charge drops to a specific fraction of its initial value. **Key Concepts:** 1. **RC Circuit Dynamics:** - When the switch is closed, the circuit begins to discharge. - The current (\( I(t) \)) and the charge (\( Q(t) \)) on the capacitor change over time based on exponential decay. 2. **Capacitor Charge Equation:** - \( Q(t) = Q_0 \cdot e^{-t/(RC)} \) where \( Q_0 = C \cdot V_0 \). 3. **Current Equation:** - \( I(t) = \frac{V_0}{R} \cdot e^{-t/(RC)} \). 4. **Given Condition:** - The problem states \( Q(t) = \frac{1}{7}Q_0 \). - Use this condition to find \( t \) and subsequently find \( I(t) \). 5. **Steps to Solve:** - Compute \( Q_0 = C \cdot V_0 \). - Substitute \( Q(t) = \frac{1}{7}Q_0 \) into \( Q(t) = Q_0 \cdot e^{-t/(RC)} \) to solve for \( t \). - Substitute \( t \) back into \( I(t) = \frac{V_0}{R} \cdot e^{-t/(RC)} \) to find the current at that time. This exercise
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
DC circuits
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.
Similar questions
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
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…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS