EGR 203 Electric and Electronic Circuits Assignment 9

  1. Given the circuit below, with R=22.8 kΩ and C = 10 nF. Find the time constant τ and the equation for the voltage across the capacitor as a function of time if the voltage input is 2 V for t ≤ 0 and 5 V for t > 0. Plot the results for a time of at least five time constants.

  2. Do the problem above in Multisim, using a pulse source and both oscillocope simulation and transient analysis (see RC_multisim.ppt).

  3. Suppose I measured the rise time as a function of the resistance in an RC circuit. The capacitor was nominally 0.2 µF and the signal generator panel says that the equivalent resistance of the device is 50 Ω. The results I found are shown in the following table.

    R (Ω)rise time
    1000470 µs
    2000920 µs
    30001.32 msec
    40001.82 msec

    Plot this data and fit a straight line to the plot. The slope should be proportional to the capacitance and the x-intercept should be the negative of the equivalent resistance of the signal generator. Find these values and compare them to the nominal values. Note that rise time is 2.2τ.

  4. Suppose we have a coil of 600 turns of copper wire wrapped around a wooden spool 1.2 cm in diameter and 0.8 cm long. Assume that the relative permeability of wood is one. Find the inductance of this coil

  5. If we have a current of 500 mA flowing through and inductance of 12 mH, find the magnetic flux through the coil and the energy stored in the magnetic field.

  6. Given two inductances, 8 mH and 24 mH, find the equivalent inductance if they are connected in parallel and then if they are in series.

  7. Find the energy stored in each capacitor and inductor, under steady-state conditions, in the circuit below.
    Assume V0 = 6 V, L = 2 H, C1 = 2 F, C2 = 1 F, C3 = 3 F, R1 = 2 Ω, R2 = 4 Ω, R3 = 6 Ω, and R4 = 8 Ω,

  8. Let z1 = 11 - 22j,
    z2 = 9 + 14j,
    z3 = 10 - 24j, and
    z4 = 25 + 17j    . Find
    1. zp = 1/(1/z1 + 1/z2)
    2. zs = z3 + z4
    3. vout = zs/(zs+zp) vin, where vin = 140 V at 40 degrees (that is, 140cos(ωt+40 deg))

  9. Let v(t) = 15 cos(2400t)+ 20 sin(2400t). Express v(t) in the form Vmcos(ωt-φ). Find the frequency of the voltage signal, the peak voltage (not peak-to-peak), the rms voltage, and the phase angle in degrees. Hint: Convert cartesian (15, 20) to polar coordinates.

Maintained by John Loomis, last updated 18 April 2011