The output voltage of an AC generator is given by Delta ? = (100 V) sin (50 pi t

Question

The output voltage of an AC generator is given by Delta ? = (100 V) sin (50 pi t). The generator is connected across a 19 ohm resistor. By inspection, what are the following? maximum voltage frequency rms voltage across the resistor rms current in the resistor maximum current in the resistor power delivered to the resistor Should the argument of the sine function be in degrees or radians? The argument of the sine function should be in degrees. The argument of the sine function should be in radians. Compute the current when t = 0.0050 s

Explanation / Answer

   Compare the given equation to standardequation of AC voltage    V   =   V0* sin ( * t)    a.   Maximumvoltage   V0   =   100   V    b.   Frequency   f   =   / 2                                  =   50 / 2                                  =   25   Hz    c.   RMSvoltage   Vrms   =   V0/ 2                                           =   100/ 2                                           =   70.71      V    d.   RMScurrent   Irms   =   Vrms/ R                                        =   70.71/ 19                                            =   3.72   A    e.   Maximumcurrent   I0   =   V0/ R                                              =   100/ 19                                              =   5.26   A    f.   Power   P   =   Vrms2/ R                            =   70.712/ 19                            =   263.15   W    f   .   radians
   g.   I0.0050   =   V0.0050/ R                      =   100* sin (50 * 3.14 * 0.0050) / 19                      =   3.72   A

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