An ac generator with emf amplitude Em = 240 V and operating at frequency 360 Hz

Question

An ac generator with emf amplitude Em = 240 V and operating at frequency 360 Hz causes oscillations in a series RLC circuit having R = 180 , L = 350 mH, and C = 140 F.

(a) Determine the impedance Z.

(b) Determine the phase .

(c) Determine the current amplitude I.

(d) Completely determine i(t).

These are my teachers requirements if you could please follow them I would really appreciate it thank you :)

In addition to being neat and clear, and actually answering the question, you must:

1) show the original principle (often in equation form)

2) substitute variables as needed

3) solve it first (before substituting numbers)

4) show every substitution (with units and correct sig figs)

5) present a boxed answer (with units and correct sig figs)

In a Force problem in more than one dimension, you MUST start with a Free Body Diagram.

Explanation / Answer

a)     inductive reactance = wL

                                        = 2 * 3.14 * 360 * 0.350

                                         = 791.28 ohm

      capacitive reactance = 1/wC

                                        = 1/(2 * 3.14 * 360 * 140 * 10-6)

                                         =   3.159

=>   impedance = sqrt(1802 + (791.28 - 3.159)2)

                             =   808.41 ohm

b)    phase    = tan-1[(791.28 - 3.159)/180]

                       =   77.13   degree

c)    current amplitude I =   240/808.41

                                       =   0.2968 A

d)   i(t)   = 0.2968 * sin(2260.8t + 77.13o)

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