Consider a Series RLC circuit [Resistor (R, ohms ())- Inductor (L, Henrys) Capacitor (C, Farad)]

Figure 3 - RLC Circuit

Basic circuit values:

• Circular line frequency: =2f=100, rad/sec

• AC period: T=1f=0.02 sec

The following relationships apply:

• Applied Voltage: Vt=Eo sint, V

• Current Amplitude: A=EoL2- 1 C2+ R2 2, amps

• Current Phase Angle: =atan LR-1RC , rad

• Total Current: It =A sint-, amps

• Resistor Voltage Drop: VRt =R A sint-, V

• Inductor Voltage Drop: VLt =L A cost-, V

• Capacitor Voltage Drop: VCt=-A C cost-, V

Exercises/Questions:

Write a program that will loop through a time interval equal to 2 AC periods in t increments.

t can be calculated by assuming 20 pts/period and using the circuit period.

At each timestep do the following:

• Make separate function calls to compute the total current in the circuit, resistor voltage drop, inductor voltage drop and capacitor voltage drop

• Verify at Kirchhoff's Voltage Law at each timestep: Vt=VRt+VLt+VCt

• Output in column format the following values:

  • Vt

  • It

  • VRt

  • VLt

  • VCt

Prompt the user to input the circuit element values and other problem statement parameters:

• Applied voltage amplitude (Eo) volts

• Line frequency (f) hertz (= 1/sec)

• Resistor value (R) ohms (W)

• Inductor value (L) henrys

• Capacitor value (C) F

• pts/AC period (nstep)

NOTE: YOU MUST RUN THE CASE WHERE THE INPUT VALUES MATCH THOSE SPECIFIED IN FIGURE 3. YOU ARE FREE TO RUN OTHER CASES BUT YOU MUST COMPLETE THE FIGURE 3 CASE

Sample Output for given circuit:

RLC Circuit Summary:

Voltage: 25-Volts @ 50-Hz

Resistor Value: 50-ohms

Inductor Value: 0.3-H

Capacitor Value: 1.5e-005-F

Calculated Parameters:

Current Amplitude: 0.195-amps

Phase Angle: -67.029-degrees

Iter.Time AV I VR VL VC VT Vdiff

0 0.000 0.000 0.180 8.983 7.177 -16.160 -0.000 0.00

1 0.001 7.725 0.194 9.720 1.594 -3.588 7.725 0.00

2 0.002 14.695 0.190 9.505 -4.146 9.335 14.695 0.00

3 0.003 20.225 0.167 8.361 -9.480 21.345 20.225 0.00

4 0.004 23.776 0.128 6.397 -13.886 31.265 23.776 0.00

5 0.005 25.000 0.076 3.808 -16.932 38.125 25.000 0.00

6 0.006 23.776 0.017 0.845 -18.322 41.253 23.776 0.00

7 0.007 20.225 -0.044 -2.200 -17.917 40.342 20.225 0.00

8 0.008 14.695 -0.101 -5.029 -15.759 35.483 14.695 0.00

9 0.009 7.725 -0.147 -7.367 -12.058 27.150 7.725 0.00

10 0.010 -0.000 -0.180 -8.983 -7.177 16.160 -0.000 -0.00

11 0.011 -7.725 -0.194 -9.720 -1.594 3.588 -7.725 -0.00

12 0.012 -14.695 -0.190 -9.505 4.146 -9.335 -14.695 0.00

13 0.013 -20.225 -0.167 -8.361 9.480 -21.345 -20.225 -0.00

14 0.014 -23.776 -0.128 -6.397 13.886 -31.265 -23.776 -0.00

15 0.015 -25.000 -0.076 -3.808 16.932 -38.125 -25.000 -0.00

16 0.016 -23.776 -0.017 -0.845 18.322 -41.253 -23.776 0.00

17 0.017 -20.225 0.044 2.200 17.917 -40.342 -20.225 -0.00

18 0.018 -14.695 0.101 5.029 15.759 -35.483 -14.695 -0.00

19 0.019 -7.725 0.147 7.367 12.058 -27.150 -7.725 0.00

20 0.020 0.000 0.180 8.983 7.177 -16.160 0.000 -0.00

21 0.021 7.725 0.194 9.720 1.594 -3.588 7.725 -0.00

22 0.022 14.695 0.190 9.505 -4.146 9.335 14.695 -0.00

23 0.023 20.225 0.167 8.361 -9.480 21.345 20.225 0.00

24 0.024 23.776 0.128 6.397 -13.886 31.265 23.776 -0.00

25 0.025 25.000 0.076 3.808 -16.932 38.125 25.000 0.00

26 0.026 23.776 0.017 0.845 -18.322 41.253 23.776 0.00

27 0.027 20.225 -0.044 -2.200 -17.917 40.342 20.225 -0.00

28 0.028 14.695 -0.101 -5.029 -15.759 35.483 14.695 0.00

29 0.029 7.725 -0.147 -7.367 -12.058 27.150 7.725 0.00

30 0.030 -0.000 -0.180 -8.983 -7.177 16.160 -0.000 0.00

31 0.031 -7.725 -0.194 -9.720 -1.594 3.588 -7.725 0.00

32 0.032 -14.695 -0.190 -9.505 4.146 -9.335 -14.695 0.00

33 0.033 -20.225 -0.167 -8.361 9.480 -21.345 -20.225 -0.00

34 0.034 -23.776 -0.128 -6.397 13.886 -31.265 -23.776 -0.00

35 0.035 -25.000 -0.076 -3.808 16.932 -38.125 -25.000 -0.00

36 0.036 -23.776 -0.017 -0.845 18.322 -41.253 -23.776 -0.00

37 0.037 -20.225 0.044 2.200 17.917 -40.342 -20.225 -0.00

38 0.038 -14.695 0.101 5.029 15.759 -35.483 -14.695 -0.00

39 0.039 -7.725 0.147 7.367 12.058 -27.150 -7.725 0.00

Suggestions:

Consider the following general structure for your program:

• Declare and initialize variables to represent any or all of the following:

• double R, L, C, A, , f, , Eo, T, t;

• int nstep; // #timesteps/cycle

• Consider developing functions to perform the following tasks:

  • Convert the frequency to a omega

  • Calculate the period from the frequency

  • Calculate the current magnitude

  • Calculate the current theta.

  • Calculate the applied voltage for the current t period

  • Calculate the total current for the current t period

  • Calculate the resistor voltage for the current t period

  • Calculate the inductor voltage for the current t period

  • Calculate the capacitor voltage for the current t period

Note: You are required to develop at least 5 functions to create your RLC solver.

• In main(), declare automatic (double) variables:

  • t current time in cycle, sec

  • I total current in circuit, amps

  • VR resistor voltage drop, V

  • VL inductor voltage drop, V

  • VC capacitor voltage drop, V

• Set up a loop in main() that loops through 2 AC periods/cycles in increments of t (obtain 20 values/period).

• Inside the loop call the appropriate functions to calculate and display in tabular form the values of VR, VL, VC, etc...

R-50 L-0.3 H Eo 25 V f-50 Hz R-50 L-0.3 H Eo 25 V f-50 Hz