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Skyler MacDougall

Homework 1: Due 1/22/2020

 1.  Draw a waveshape of a sinusoidal voltage having a peak value of 200V and a frequency of 5Hz.
     ![homework1question10](hw1q10.PNG)

 2.  If the voltage is zero at $t=0$, what is the voltage at $t=5ms$? $75ms$?$150ms$?

     | Time (t, ms) | Voltage (V)   |
     | ------------ | ------------- |
     | 5            | $\approx31$   |
     | 75           | $\approx 141$ |
     | 150          | $-200$        |

  1. A sinusoidal current has an effective value of 50A. Calculate the peak value of current. 50A*{\sqrt{2}\over2}\approx35A

  2. A sinusoidal voltage of 120V is applied to a 10\Omega resistor. Calculate

    1. the effective current through the resistor.

      {120V\over 10\Omega}=12A

  3. the peak voltage across the resistor.

    120V*\sqrt{2}\approx170V_{RMS}

    1. the power dissipated by the resistor. 120V*12A=1440W

    2. The peak power dissipated by the resistor. 170V_{RMS}(12A\sqrt{2})=2880W

  4. A distorted voltage contains an 11^th^ harmonic of 20V, 253Hz. Calcultate the frequency of the fundamental.

    235Hz*11^{th}Harmonic\approx2.6kHz

  5. The current in a 60Hz single phase motor lags 36 degrees behind the voltage. Calculate the time interval between positive peaks of voltage and current.

    {1\over \cancel{60Hz}}*{\cancel{360^\circ}6^\circ\over 36^\circ}={1\over 6}seconds=0.1\overline{66}seconds

  6. Determine the phase angle between the following phasors and, in each case, indicate which phasor is lagging.

    homework1question13

    1. I_1 and I_3

      \angle I_1-\angle I_3=-60^\circ\ \therefore\ I_1 lags I_3by60^\circ

  7. I_2 and I_3

    \angle I_2-\angle I_3=-90^\circ\ \therefore\ I_2 lags I_3 by 90^\circ

  8. E and I_1

    \angle E - \angle I_1=-150^\circ\ \therefore\ ElagsI_1by150^\circ

  9. The voltage applied to an AC magnet is given by the expression E=160sin\phi, and the current is I=20sin(\phi-60^\circ), all angles being expressed in degrees.

    1. Draw the phasor diagram for E and I, using effective values.

      homework1q16_2

    2. Draw the waveshape of E and I as a function of \phi.

      homework1q15

    3. Calculate the peak positive power and the peak negative power in the circuit.