Question Pre-2: In Figure 8. 1, suppose the switch is initial is completely discharged, and the power supply is set to a c then flipped to Position 1. After flipping the switch, how many time constants must el. capacitor reaches 39%, 63%, and 86% of Vo? Lab 8: Time-De
Question Pre-2: In Figure 8. 1, suppose the switch is initial is completely discharged, and the power supply is set to a c then flipped to Position 1. After flipping the switch, how many time constants must el. capacitor reaches 39%, 63%, and 86% of Vo? Lab 8: Time-De
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Transcribed Image Text:**Lab 8: Time-Dependent Circuits**
**Question Pre-2:** In Figure 8.1, suppose the switch is initially set to Position 2, the capacitor is completely discharged, and the power supply is set to a constant voltage \( V_0 \). The switch is then flipped to Position 1.
After flipping the switch, how many time constants must elapse before the voltage across the capacitor reaches 39%, 63%, and 86% of \( V_0 \)?
**Explanation:**
This exercise examines the charging process of a capacitor in a circuit when a switch changes positions. The question involves calculating the time required for the capacitor to reach certain percentages of the maximum voltage \( V_0 \), which is contingent on the time constant of the circuit, a crucial component for understanding exponential growth in electrical circuits.
Due to the angle of the image, the specific illustration of Figure 8.1 is not visible, but it likely represents a basic RC (resistor-capacitor) circuit that showcases how the voltage changes over time as the capacitor charges.
The percentages given suggest the use of the charging formula for capacitors: \( V(t) = V_0 (1 - e^{-t/RC}) \), where \( RC \) is the time constant. Solving for these specific percentages will deepen the user's understanding of exponential growth behaviors in RC circuits.
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Step 1: Introduction
This is a question from the charging of capacitor in a series RC circuit in DC power supply. Its answer can be given as follows__
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