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A capacitor of capacitance C = 7.5 μF is initially uncharged. It is connected in series with a switch of negligible resistance, a resistor of resistance R = 11.5 kΩ, and a battery which provides a potential difference of VB = 110 V. (a)  Calculate the time constant τ for the circuit in seconds.  (b)  After a very long time after the switch has been closed, what is the voltage drop VC across the capacitor in terms of VB?  (c)  Calculate the charge Q on the capacitor a very long time after the switch has been closed in C.

A capacitor of capacitance C = 7.5 μF is initially uncharged. It is connected in series with a switch of negligible resistance, a resistor of resistance R = 11.5 kΩ, and a battery which provides a potential difference of VB = 110 V. (a)  Calculate the time constant τ for the circuit in seconds.  (b)  After a very long time after the switch has been closed, what is the voltage drop VC across the capacitor in terms of VB?  (c)  Calculate the charge Q on the capacitor a very long time after the switch has been closed in C.

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)...
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A capacitor of capacitance C = 7.5 μF is initially uncharged. It is connected in series with a switch of negligible resistance, a resistor of resistance R = 11.5 kΩ, and a battery which provides a potential difference of VB = 110 V.

(a)  Calculate the time constant τ for the circuit in seconds. 

(b)  After a very long time after the switch has been closed, what is the voltage drop VC across the capacitor in terms of VB? 

(c)  Calculate the charge Q on the capacitor a very long time after the switch has been closed in C. 

### Description of a Simple RC Circuit This diagram depicts a basic RC (Resistor-Capacitor) circuit, commonly used in electronics studies to demonstrate the charging and discharging behavior of a capacitor. #### Components of the Circuit: 1. **Capacitor (C)**: - A device that stores electrical energy in an electric field. It is represented by two parallel lines, one curved and one straight in this diagram, labeled as "C". 2. **Resistor (R)**: - An electrical component that limits or regulates the flow of electrical current in an electronic circuit. It is depicted as a zigzag line in the circuit, labeled as "R". 3. **Switch (S)**: - A device for making and breaking the connection in an electric circuit. It is represented by a break in the line that can be connected, labeled as "S". 4. **Battery (VB)**: - The power source of the circuit. It is represented with a long and a short parallel line, which denotes the positive and negative terminals respectively, labeled as "VB". #### Circuit Layout: - The switch (S) is connected in series with the capacitor (C) and the resistor (R). - The battery (VB) is connected in series with this combined RC network. #### Functionality: - When the switch (S) is closed, the circuit allows current to flow from the battery (VB) through the resistor (R) and into the capacitor (C). - The capacitor (C) will start to charge up, with the voltage across the capacitor increasing over time. - Eventually, the voltage across the capacitor will equal the voltage of the battery, and the current flow will stop as the capacitor is fully charged. - If the switch (S) is opened, the capacitor will begin to discharge through the resistor. #### Applications: - RC circuits are fundamental in the design of electronic filters, timers, and in the development of signal processing circuits. Understanding the behavior of such a simple RC circuit is crucial in the study of more complex electronic systems and signal processing applications.
Transcribed Image Text:### Description of a Simple RC Circuit This diagram depicts a basic RC (Resistor-Capacitor) circuit, commonly used in electronics studies to demonstrate the charging and discharging behavior of a capacitor. #### Components of the Circuit: 1. **Capacitor (C)**: - A device that stores electrical energy in an electric field. It is represented by two parallel lines, one curved and one straight in this diagram, labeled as "C". 2. **Resistor (R)**: - An electrical component that limits or regulates the flow of electrical current in an electronic circuit. It is depicted as a zigzag line in the circuit, labeled as "R". 3. **Switch (S)**: - A device for making and breaking the connection in an electric circuit. It is represented by a break in the line that can be connected, labeled as "S". 4. **Battery (VB)**: - The power source of the circuit. It is represented with a long and a short parallel line, which denotes the positive and negative terminals respectively, labeled as "VB". #### Circuit Layout: - The switch (S) is connected in series with the capacitor (C) and the resistor (R). - The battery (VB) is connected in series with this combined RC network. #### Functionality: - When the switch (S) is closed, the circuit allows current to flow from the battery (VB) through the resistor (R) and into the capacitor (C). - The capacitor (C) will start to charge up, with the voltage across the capacitor increasing over time. - Eventually, the voltage across the capacitor will equal the voltage of the battery, and the current flow will stop as the capacitor is fully charged. - If the switch (S) is opened, the capacitor will begin to discharge through the resistor. #### Applications: - RC circuits are fundamental in the design of electronic filters, timers, and in the development of signal processing circuits. Understanding the behavior of such a simple RC circuit is crucial in the study of more complex electronic systems and signal processing applications.
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