College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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**RC Circuit Analysis for Educational Purpose** **Question 2**: An RC circuit with a 1000 V battery is connected to a fluorescent lamp as shown in the figure. The lamp turns on when the voltage across the capacitor reaches 80.0 V, which happens after 10 seconds after the switch is closed. If \( R = 3 \, \text{M}\Omega \), (a) what is the value of the capacitance \( C \)? (b) If we have to switch the lamps 4 times in a second, what should be the value of capacitance? **Diagram Description**: - The diagram illustrates a simple RC circuit. - The components shown include a battery with a voltage of 1000 V, a resistor \( R \), a capacitor \( C \), and a switch \( S \). - The lamp is placed in parallel with the capacitor. - The circuit is closed when the switch \( S \) is engaged. **Key Problem Solving Steps**: 1. **Understand the working of RC Circuits**: The time constant \(\tau\) of an RC circuit is given by \(\tau = RC\). 2. **Examine the voltage equation**: When the switch is closed, the charge on the capacitor grows as \( V(t) = V_0(1 - e^{-t/RC}) \). 3. **Calculate for Part (a)**: - Set \( V(t) = 80.0 \, \text{V} \) at \( t = 10 \, \text{seconds} \). - Use the formula to determine \( C \). 4. **Discuss Part (b)**: - For the lamp to switch 4 times a second, calculate how this frequency affects the charging and discharging cycle, and adjust the capacitance \( C \) accordingly. This problem is an excellent exercise in understanding transient analysis in RC circuits, emphasizing the relationship between resistance, capacitance, and the time constant.
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Transcribed Image Text:**RC Circuit Analysis for Educational Purpose** **Question 2**: An RC circuit with a 1000 V battery is connected to a fluorescent lamp as shown in the figure. The lamp turns on when the voltage across the capacitor reaches 80.0 V, which happens after 10 seconds after the switch is closed. If \( R = 3 \, \text{M}\Omega \), (a) what is the value of the capacitance \( C \)? (b) If we have to switch the lamps 4 times in a second, what should be the value of capacitance? **Diagram Description**: - The diagram illustrates a simple RC circuit. - The components shown include a battery with a voltage of 1000 V, a resistor \( R \), a capacitor \( C \), and a switch \( S \). - The lamp is placed in parallel with the capacitor. - The circuit is closed when the switch \( S \) is engaged. **Key Problem Solving Steps**: 1. **Understand the working of RC Circuits**: The time constant \(\tau\) of an RC circuit is given by \(\tau = RC\). 2. **Examine the voltage equation**: When the switch is closed, the charge on the capacitor grows as \( V(t) = V_0(1 - e^{-t/RC}) \). 3. **Calculate for Part (a)**: - Set \( V(t) = 80.0 \, \text{V} \) at \( t = 10 \, \text{seconds} \). - Use the formula to determine \( C \). 4. **Discuss Part (b)**: - For the lamp to switch 4 times a second, calculate how this frequency affects the charging and discharging cycle, and adjust the capacitance \( C \) accordingly. This problem is an excellent exercise in understanding transient analysis in RC circuits, emphasizing the relationship between resistance, capacitance, and the time constant.
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Step 1

Given,

An RC circuit with

Voltage V=100V

Voltage V0=80V

Time t=1s

Resistance R=3M Ω

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