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1. The figure below shows an RC circuit consists of uncharged capacitor C = 500 µF resistor R1 = 3.50 ko and ideal battery of emf ɛ = 210 V and open switch, S. At t= 0 s, the switch is flipped to position a. When the switch is in position b, the capacitor is disconnected from the ideal battery and R1 and is connected and resistor, R2 = 12.2 kn. S a R2

1. The figure below shows an RC circuit consists of uncharged capacitor C = 500 µF resistor R1 = 3.50 ko and ideal battery of emf ɛ = 210 V and open switch, S. At t= 0 s, the switch is flipped to position a. When the switch is in position b, the capacitor is disconnected from the ideal battery and R1 and is connected and resistor, R2 = 12.2 kn. S a R2

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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**Problem Statement:** d. At the instant the capacitor is charged to 87% of its maximum charge, the switch \( S \) is flipped from to position \( b \). What is the current through \( R_2 \) immediately after the switch is flipped to position \( b \)? **Explanation:** In this problem, we are considering an electric circuit containing a capacitor and resistors. At a certain moment, the capacitor is charged to 87% of its maximum capacity. Initially, a switch labeled \( S \) is positioned such that it facilitates the charging of the capacitor. **Key Concepts:** - **Capacitors** store electrical energy and release it when needed. They charge and discharge according to the circuit they are in. - **Resistors** (\( R_2 \) here) control the flow of current in the circuit. - **Switches** alter the configuration of the circuit by changing their position, which affects current flow and potential differences. **Objective:** We need to determine the initial current through \( R_2 \) when the switch \( S \) changes to position \( b \). This involves understanding the discharge of the capacitor and applying relevant electrical formulas to find the current through \( R_2 \). **Analysis Steps:** 1. **Initial Charge**: Calculate the initial charge \( Q \) on the capacitor, which is 87% of its maximum charge \( Q_{\text{max}} \). 2. **Circuit Analysis**: After the switch changes to position \( b \), analyze how the circuit configuration affects current flow. Use Ohm’s Law and Kirchhoff's rules as needed. 3. **Current Calculation**: Use the known properties of capacitive discharge to calculate the instantaneous current through \( R_2 \). In theoretical studies or practical applications, solving such problems requires understanding of transient electrical responses in capacitive circuits and applying the correct mathematical models.
Transcribed Image Text:**Problem Statement:** d. At the instant the capacitor is charged to 87% of its maximum charge, the switch \( S \) is flipped from to position \( b \). What is the current through \( R_2 \) immediately after the switch is flipped to position \( b \)? **Explanation:** In this problem, we are considering an electric circuit containing a capacitor and resistors. At a certain moment, the capacitor is charged to 87% of its maximum capacity. Initially, a switch labeled \( S \) is positioned such that it facilitates the charging of the capacitor. **Key Concepts:** - **Capacitors** store electrical energy and release it when needed. They charge and discharge according to the circuit they are in. - **Resistors** (\( R_2 \) here) control the flow of current in the circuit. - **Switches** alter the configuration of the circuit by changing their position, which affects current flow and potential differences. **Objective:** We need to determine the initial current through \( R_2 \) when the switch \( S \) changes to position \( b \). This involves understanding the discharge of the capacitor and applying relevant electrical formulas to find the current through \( R_2 \). **Analysis Steps:** 1. **Initial Charge**: Calculate the initial charge \( Q \) on the capacitor, which is 87% of its maximum charge \( Q_{\text{max}} \). 2. **Circuit Analysis**: After the switch changes to position \( b \), analyze how the circuit configuration affects current flow. Use Ohm’s Law and Kirchhoff's rules as needed. 3. **Current Calculation**: Use the known properties of capacitive discharge to calculate the instantaneous current through \( R_2 \). In theoretical studies or practical applications, solving such problems requires understanding of transient electrical responses in capacitive circuits and applying the correct mathematical models.
The image illustrates an RC circuit with various components. Here's a detailed transcription and explanation: 1. **Text Description:** The circuit contains: - An uncharged capacitor, \( C = 500 \, \mu\text{F} \). - A resistor, \( R_1 = 3.50 \, \text{k}\Omega \). - An ideal battery with an electromotive force (emf) \( \varepsilon = 210 \, \text{V} \). - An open switch, \( S \). At time \( t = 0 \, \text{s} \), the switch is flipped to position \( a \). When the switch is in position \( b \), the capacitor is disconnected from the ideal battery and \( R_1 \), and instead is connected to another resistor, \( R_2 = 12.2 \, \text{k}\Omega \). 2. **Diagram Explanation:** - **Battery (\(\varepsilon\))**: Provides a potential difference of 210 V, connected to the circuit when the switch \( S \) is in position \( a \). - **Switch (\(S\))**: A pivot switch with two positions, \( a \) and \( b \). - *Position \( a \)*: Connects the capacitor \( C \) to the battery and resistor \( R_1 \). - *Position \( b \)*: Connects the capacitor \( C \) to the resistor \( R_2 \), isolating it from the battery. - **Capacitor (\(C\))**: Initially uncharged, it charges when the switch is in position \( a \) and discharges through \( R_2 \) when the switch is in position \( b \). - **Resistor \(R_1\) and \(R_2\)**: Provide resistance in the circuit path during different switch positions. This setup demonstrates how an RC circuit can function with different configurations based on the position of the switch, illustrating charging and discharging cycles of the capacitor.
Transcribed Image Text:The image illustrates an RC circuit with various components. Here's a detailed transcription and explanation: 1. **Text Description:** The circuit contains: - An uncharged capacitor, \( C = 500 \, \mu\text{F} \). - A resistor, \( R_1 = 3.50 \, \text{k}\Omega \). - An ideal battery with an electromotive force (emf) \( \varepsilon = 210 \, \text{V} \). - An open switch, \( S \). At time \( t = 0 \, \text{s} \), the switch is flipped to position \( a \). When the switch is in position \( b \), the capacitor is disconnected from the ideal battery and \( R_1 \), and instead is connected to another resistor, \( R_2 = 12.2 \, \text{k}\Omega \). 2. **Diagram Explanation:** - **Battery (\(\varepsilon\))**: Provides a potential difference of 210 V, connected to the circuit when the switch \( S \) is in position \( a \). - **Switch (\(S\))**: A pivot switch with two positions, \( a \) and \( b \). - *Position \( a \)*: Connects the capacitor \( C \) to the battery and resistor \( R_1 \). - *Position \( b \)*: Connects the capacitor \( C \) to the resistor \( R_2 \), isolating it from the battery. - **Capacitor (\(C\))**: Initially uncharged, it charges when the switch is in position \( a \) and discharges through \( R_2 \) when the switch is in position \( b \). - **Resistor \(R_1\) and \(R_2\)**: Provide resistance in the circuit path during different switch positions. This setup demonstrates how an RC circuit can function with different configurations based on the position of the switch, illustrating charging and discharging cycles of the capacitor.
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