Capacitors Prelab Notes

UNIVERSITY OF COLORADO – COLORADO SPRINGS Capacitors - Prelab Notes

General Information

  • Course Name: PES 2150 - Physics Laboratory II
  • Author: Kaylee Bruce

Questions and Explanations on the RC Circuit Graphs

1. Voltage Across the Resistor (Blue Graph) - VR vs. Time

  • a) Describe the point when the switch was closed.

    • The switch is said to be closed at the moment the charge across the capacitor begins to decrease exponentially.

  • b) The time between the switch beginning closed and saturation.

    • As time progresses after the switch closes, the charge across the capacitor increases exponentially, leading to a corresponding decrease in voltage across the resistor (VR).

  • c) At any point in saturation.

    • At saturation, the voltage across the resistor (VR) is zero. This occurs because the capacitor behaves like an open system, preventing current flow to the resistor.
2. Voltage Across the Capacitor (Red Graph) - VC vs. Time

  • a) Describe the point when the switch was closed.

    • The switch closes when the charge on the capacitor begins to increase exponentially.

  • b) The time between the switch beginning closed and saturation.

    • Initially, the charge increases slowly. However, as the capacitor approaches saturation, the charge increases exponentially.

  • c) At any point in saturation.

    • In saturation, the capacitor is fully charged, acting as an open circuit, thus preventing any further charge from increasing.

Examination of RC Circuit Graph

3. Analysis of Curves and Calculation of Time Constants

  • a) Determine t from each curve - VR and VC:

    • For voltage across the resistor (VR); $t_{VR} = 1/25.6 = 0.039 ext{ s}$
    • For voltage across the capacitor (VC); $t_{VC} = 1/26.1 = 0.038 ext{ s}$

  • b) Calculate the capacitance if the resistor has a value of 120 Ω:

    • Given the formula relating the time constant to resistance and capacitance:
      au=RimesCau = R imes C
    • Rearranging gives:
      C = rac{ au}{R}
    • Substituting the calculated time constant:
      C = rac{0.038}{120} = 3.17 imes 10^{-7} F
    • Note: The result indicates the capacitance in Farads.

  • c) Defend your calculations with a quick description of the process:

    • The time constant ($ au$) was first determined from the curves corresponding to VR and VC. This value was then plugged into the formula for capacitance, where the resistance of 120 ohms is used, leading to the determination of capacitance in relation to how charge and voltage are defined in the context of capacitive circuits.

Additional Notes

  • Conceptual Understanding:
    • Capacitance (C) is defined as the ability of a system to store charge per unit voltage, quantitatively given by the relationship:
      C = rac{Q}{V} where Q is the charge in coulombs and V is the voltage in volts.
  • Capacitors in RC circuits are fundamental to understanding charge and discharge rates, which are key to circuit behavior in electronics. Common applications include timing circuits and filters.

Conclusion

  • This explores the dynamics of the RC circuit when subjected to voltage changes, and it emphasizes the exponential nature of charging and discharging in capacitors. Understanding these principles is vital for further studies in electronics and circuit design.