Steady State Response of a RC Circuit with Sinusoidal Input


The figure below shows the RC circuit from example 10.6-1 of Introduction to Electric Circuits, 5e by R.C. Dorf and J.A. Svoboda. The input to this circuit is the current

provided by the current source. The response, or output, of the circuit is the voltage v(t). The network function

describes the relationship between the phasors corresponding to the input, i(t), and the output, v(t).

The steady state response of this circuit is given by

The value of the capacitance C, can be changed using the scrollbar.


Suggestions:

  1. Set C=10 mF to see the circuit in Example 10.6-1.

  2. Determine the range of phase angles of v(t) that can be obtained by varying C between 0.1 and 20 mF.

  3. As C decreases, the impedance of the capacitor increases. A large impedance acts like an open circuit. A resistor in parallel with a large impedance acts like the resistor. Verify that reducing C to 0.1 mF makes the parallel combination of the resistor and capacitor act like the 1 Ohm resistor.

  4. As C increases, the impedance of the capacitor decreases. A small impedance acts like an short circuit. A resistor in parallel with a small impedance acts like a short circuit. Does increasing C to 20 mF make the impedance of the capacitor small enough that it can be approximated as a short circuit?

  5. Vary C until v(t) is half as large as i(t). Reconsider the equations given above for i(t) and v(t) in light of the value that you found for C.

  6. Vary C until the phase difference between i(t) and v(t) is 45 degrees. Reconsider the equations given above for i(t) and v(t) in light of the value that you found for C.