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lab32 - LAB 32 Capacitors The charge q on a capacitors...

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LAB# 32 Capacitors The charge q on a capacitor’s plate is proportional to the potential difference V across the capacitor. We express this with V q C = , where C is a proportionality constant known as the capacitance . C is measured in the unit of the farad, F, (1 farad = 1 coulomb/volt). If a capacitor of capacitance C (in farads), initially charged to a potential V 0 (volts) is connected across a resistor R (in ohms), a time-dependent current will flow according to Ohm’s law. This situation is shown by the RC (resistor-capacitor) circuit below when the switch is closed. Figure 1 As the current flows, the charge q is depleted, reducing the potential across the capacitor, which in turn reduces the current. This process creates an exponentially decreasing current, modeled by . V t V e t RC ( ) = ! 0 The rate of the decrease is determined by the product RC , known as the time constant of the circuit. A large time constant means that the capacitor will discharge slowly. When the capacitor is charged, the potential across it approaches the final value exponentially, modeled by V t V e t RC ( ) = ! " # $ % & ! 0 1 . The same time constant RC describes the rate of charging as well as the rate of discharging. OBJECTIVES Measure an experimental time constant of a resistor-capacitor circuit. Compare the time constant to the value predicted from the component values of the resistance and capacitance. Measure the potential across a capacitor as a function of time as it discharges and as it charges. Fit an exponential function to the data. One of the fit parameters corresponds to an experimental time constant.
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APPARATUS Power Macintosh 100- µ F non-polarized capacitor Universal Lab Interface 10-k Ω , 400-k Ω
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