Question

10.An AC voltage source is connected in series to an inductor, a capacitor, and a resistor of 8 Ohms. At the frequency when the phase angle is zero, capacitive reactance is 7 Ohms. What is the phase angle between the current and voltage at a frequency which is a factor of 3.2 times less than this frequency? answer in degresss and if negative

6. the resistance of a coil spun in a generator is 2 Ohms. the coil is in a magnetic field of 7.3 milli-tesla. if the coil is square with sides of 0.5 meteres and it is wound 29 times what does its frequency of spin, in Hz,need to be in order to produce a maximum current of 6 amps

Answer 1

phase angle = tan^-1(X_c-X_l)
where X_c is capacitive reactance and X_l is inductve reactance.
For zero phase angel X_c = X_l = 7 ohms
Xc is inversely proportional to frequency and X_l is directly proportional to frequency.
At frequency that is 3.2 time less than frequency, at which phase angle is zero,
Xc = 7*3.2 = 22.4
Xl = 7/3.2 = 2.2
phas angle = tan^-1 ((22.4-2.2)/8 ) = 68.4 deg

Maximum current, Im = Vm/R
                                   = BAnw/R   ( B is magnetic field, A is area of coil, n is number of turns)
                              w = Im R/ BAn
                                  = 6*2/7.3x10^-3*0.25*29
                                   = 226.7 rad/sec
                               f = w/2 pi = 36.1 Hz