A circuit is constructed with an AC generator, a capacitor and a resistor as shown below (figure credit: Serway and Jewett). The generator on the left provides a source of emf that varies as a function of time, Avin - Vo sin wt. We connect the two leads on the right to an ocilloscope in order measure the voltage across the resistor, Avout, as a function of time.

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A circuit is constructed with an AC generator, a capacitor and a resistor as shown below (figure credit: Serway and Jewett). The generator on the left provides a source of emf that varies as a function of time, Avin = Vo sin wt. We connect the two leads on the right to an
ocilloscope in order to measure the voltage across the resistor, Avout, as a function of time.
Avin
R.
Avout
(a) First, write an expression for the current in the circuit as a function of time. You can use Vo, w, C, and R in your answer. If you define any other quantities, they should be written in terms of these variables.
(b) Now use your answer from part (a) to get the potential difference across the resistor, again as a function of time. Do you expect the waveform of Avout to be in phase, ahead of, or behind the input voltage Avin?
(c) Finally, write the ratio of the amplitude of the output voltage Avout to that of the input voltage Avin: (The amplitude of the input voltage is just Vo.) This ratio should depend on the generator frequency w, and represents how much signal gets transmitted to the output given a
particular input. Does this circuit tend to "let through" much signal for high frequencies? What about for low frequencies? See if you can understand why we call such a setup a filter.
Transcribed Image Text:A circuit is constructed with an AC generator, a capacitor and a resistor as shown below (figure credit: Serway and Jewett). The generator on the left provides a source of emf that varies as a function of time, Avin = Vo sin wt. We connect the two leads on the right to an ocilloscope in order to measure the voltage across the resistor, Avout, as a function of time. Avin R. Avout (a) First, write an expression for the current in the circuit as a function of time. You can use Vo, w, C, and R in your answer. If you define any other quantities, they should be written in terms of these variables. (b) Now use your answer from part (a) to get the potential difference across the resistor, again as a function of time. Do you expect the waveform of Avout to be in phase, ahead of, or behind the input voltage Avin? (c) Finally, write the ratio of the amplitude of the output voltage Avout to that of the input voltage Avin: (The amplitude of the input voltage is just Vo.) This ratio should depend on the generator frequency w, and represents how much signal gets transmitted to the output given a particular input. Does this circuit tend to "let through" much signal for high frequencies? What about for low frequencies? See if you can understand why we call such a setup a filter.
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