This problem has 7 parts. Please help and explain as much as possible. a) The ge

Question

This problem has 7 parts. Please help and explain as much as possible.

a) The generator in Fig.1 puts out a signal whose frequency is f = 14.30 MHz and amplitude is 8.5 V . In the circuit R = 450 mOhm, L = 15.8 nH, and C = 5.6 nF.

Complete the following by identifying the values of A, W to describe the alternating voltage description of the signal: E(t) = A (V) sin( Wt ) .

Give your answer in the form "a.b" as the value of A and "c.de x 10^(x)" as the value of W. Separate the values with a comma followed by a space. For example, if A is 1.5 and b is 1.55 x 10^(-6) then you would input your answer as 1.5, 1.55 x 10^(-6)

b) Find the capacitive reactance of the circuit. Give your answer in the form "a.bc x 10^(x)" Ohm.

c) Determine the inductive reactance of the circuit. Give your answer in the form "a.bc x 10^(x)" Ohm.

d) Determine the impedance Z of the circuit. Give your answer in the form "ab.c" milli-ohm.

e) Determine the current amplitude Imax in the circuit. Give your answer in the form "ab.c" A.

f) Determine the value of ? the phase constant for the circuit . Give your answer in the form "a.bc" radians.

g) Finally, Complete the following by inputting the values of Imax, W and ? to describe the description of the resulting current in the circuit:

                                 i(t) = Imax (A) sin( Wt - (+/-?) ) .

Note give Imax in Amperes, W in rad./s and ? in rad.

For example if I max = 25.0 A, W = 1.55 x 10^(-6) radians/s and ? = 1.6 radians, your answer should be input as   

                         25.0, 1.55 x 10^(-6), +1.6

Note that the inputs are separated by a comma followed by a space.

This problem has 7 parts. Please help and explain as much as possible. a) The generator in Fig.1 puts out a signal whose frequency is f = 14.30 MHz and amplitude is 8.5 V . In the circuit R = 450 mOhm, L = 15.8 nH, and C = 5.6 nF. Complete the following by identifying the values of A, W to describe the alternating voltage description of the signal: E(t) = A (V) sin( Wt ) . Give your answer in the form a.b as the value of A and c.de x 10^(x) as the value of W. Separate the values with a comma followed by a space. For example, if A is 1.5 and b is 1.55 x 10^(-6) then you would input your answer as 1.5, 1.55 x 10^(-6) b) Find the capacitive reactance of the circuit. Give your answer in the form a.bc x 10^(x) Ohm. c) Determine the inductive reactance of the circuit. Give your answer in the form a.bc x 10^(x) Ohm. d) Determine the impedance Z of the circuit. Give your answer in the form ab.c milli-ohm. e) Determine the current amplitude Imax in the circuit. Give your answer in the form ab.c A. f) Determine the value of ? the phase constant for the circuit . Give your answer in the form a.bc radians. g) Finally, Complete the following by inputting the values of Imax, W and ? to describe the description of the resulting current in the circuit: i(t) = Imax (A) sin( Wt - (+/-?) ) . Note give Imax in Amperes, W in rad./s and ? in rad. For example if I max = 25.0 A, W = 1.55 x 10^(-6) radians/s and ? = 1.6 radians, your answer should be input as 25.0, 1.55 x 10^(-6), +1.6 Note that the inputs are separated by a comma followed by a space.

Explanation / Answer

a)

A=8.5 Volts

W=2pi*f =2pi*(14.3*106)=8.99*107 rad/s

b)

Capacitive reactance

XC=1/WC=1/(8.985*107)(5.6*10-9)=5.03*10-1 ohms or 0.503 ohms

c)

Inductive reactance

XL=WL=(8.985*107)*(15.8*10-9)=1.42 ohms

d)

Impedance

Z=sqrt[R2+(XL-XC)2]=sqrt[0.452+(1.42-0.503)2]

Z=1.02 ohms or 1021..5 mohms

e)

Maximum Current

Imax=Vmax/Z=8.5/1.02 =8.32 A

f)

Phase Constant

o=tan-1(XL-XC/R) =tan-1(1.42-0.503/0.45)

o=63.86o

g)

I(t)=8.32Sin(8.99*107t+63.860)

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