RC Time Constant Experiment 6 Purpose: To determine the RC time constant. Equipm

Question

RC Time Constant Experiment 6 Purpose: To determine the RC time constant. Equipment Requirements: equivalent Pesistanee Voltmeter Lab timer Connecting wires Relevant Equations and Theory Charging a capacitor through a resistor Dc voltage source causes both the charge in the capacitor as well as the voltage across the capacitor to increase with time. Figure 1 shows a circuit diagram for (a) charging a capacitor (b) discharging capacitor through three resistors, connected in series. (Recall that the series of resistors the equivalent resistance RJ. In general, the voltage, y, can be expressed as a function of time b where the exponential, e 2.718 is the base of natural logarithms, t is the time, Vois the voltage of the source, and Vis the charging voltage of a capacitor; e g., in Equation 1. For the constant time constant is t RC Note that the equivalent resistance R, can used in the time is shown equation for this experiment) The rise of the voltage curve versus time exponential during the charging process of capacitor. When the time, t RC that is, one time constant, the voltage across the capacitor grows to a r" value of 1 of Vo. Hence, we can write: 0.63 V At the point that the fully charged capacitor is discharged through a resistor, the voltage across (and charge on) the capacitor "decays," and thus, decreases with time based on the following equation:

Explanation / Answer

V0 - V = V0e-(t / RC)

This is the equation when the capacitor is initially charged to a potential V0 and then it is discharging through a resistor R.

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