### Capacitor Discharge in RC CircuitThe circuit diagram shown consists of a resistor (R) and a capacitor (C) connected in series with a switch (S). The initial voltage across the capacitor is 0.15 V before the switch is closed. The resistance of the resistor is \(8.5 \times 10^6\) ohms, and the capacitance of the capacitor is 2.0 microfarads. **Problem Statement:**Determine how long, in seconds, it takes after the switch is closed for the voltage across the resistor to drop to 0.083 V.**Diagram Explanation:**- **Circuit Components:** - **R**: Resistor - **C**: Capacitor - **S**: Switch - Points B, A, C, and D indicate connections in the circuit.**Key Concepts:**- The discharge of a capacitor in an RC circuit follows an exponential decay function.- The voltage \( V(t) \) across the capacitor at time \( t \) is given by: \[ V(t) = V_0 \cdot e^{-\frac{t}{RC}} \] where: - \( V_0 \) is the initial voltage (0.15 V in this case). - \( R \) is the resistance (\(8.5 \times 10^6\) ohms). - \( C \) is the capacitance (2.0 microfarads). - \( t \) is the time in seconds.- \( RC \) is the time constant of the circuit.**Objective:**Solve for \( t \) when \( V(t) = 0.083 \) volts.

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The capacitor shown below has an initial voltage of 0.15 V before the switch is closed. The resistance is 8.5 x 106 ohms and the capacitance is 2.0 microfarads. How long after the switch is closed in seconds does it take for the voltage across the resistor to drop to 0.083 V? R www B A D

The capacitor shown below has an initial voltage of 0.15 V before the switch is closed. The resistance is 8.5 x 106 ohms and the capacitance is 2.0 microfarads. How long after the switch is closed in seconds does it take for the voltage across the resistor to drop to 0.083 V? R www B A D

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter20: Electric Potential And Capacitance

Section: Chapter Questions

Problem 46P

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