TI65 Programs Part
III: Impedance and Phase Angle of a
Series RLC Circuit, 2 x 2 Linear System Solution, Prime Factorization (from
TI65 Manual)
This is the third and final part of programs I will post
today, this Fourth of July.
Click here for Part I: Digital Root, Complex Number Multiplication, Dew Point
Click here for Part II: Reynolds Number/Hydraulic Diameter, Escape Velocity, Speed of Sound/Resonant Frequencies in an Open Pipe
TI65 Impedance and
Phase Angle of a Series RLC Circuit
Formulas:
Impedance: Z = √(R^2 + (XL –XC)^2)
Phase Angle: Φ = atan
((XL – XC)/R)
Where:
R = resistance of the resistor in ohms (Ω)
L = inductance of the inductor in Henrys (H)
C = capacitance of the capacitor in Farads (F)
f = resonance frequency in Hertz (Hz)
XL = 2*π*f*L
XC = 1/(2*π*f*C)
Program:
CODE

STEP

KEY

COMMENT

38

00

*

Start with f

2

01

2


38

02

*


2^{nd} 17

03

π


39

04

=

Calculate 2*π*f

12.0

05

STO 0


12.1

06

STO 1


38

07

*


51

08

R/S

Prompt for L

39

09

=


12.0

10

STO 0

Calculate XL

13.1

11

RCL 1


38

12

*


51

13

R/S

Prompt for C

39

14

=


34

15

1/x


12.1

16

STO 1

Calculate XC

51

17

R/S

Prompt for R

12.2

18

STO 2


2^{nd} 33

19

x^2


59

20

+


16

21

(


13.0

22

RCL 0


49

23




13.1

24

RCL 1


17

25

)


2^{nd} 33

26

x^2


39

27

=


33

28

√


2^{nd} 16

29

INV 2^{nd}
ENG

Remove ENG Notation

51

30

R/S

Display Z

16

31

(


13.0

32

RCL 0


49

33




13.1

34

RCL 1


17

35

)


28

36

÷


13.2

37

RCL 2


39

38

=


24

39

INV TAN

arctangent

51

40

R/S

Display Φ

Input: f [RST] [R/S],
L [R/S], C [R/S], R [R/S]
Result: Z [R/S] Φ
Test: f = 60 Hz, L = 0.25 H, C = 16 * 10^6 F, R = 150 Ω
Result (in degrees mode):
Z ≈ 166.18600 Ω, Φ ≈ 25.49760°
Source: Browne Ph.
D, Michael. “Schaum’s Outlines: Physics for Engineering and Science” 2^{nd} Ed. McGraw Hill: New York, 2010
TI65 2 x 2 Linear
System Solution
Let M = [ [a, b], [c, d] ],
S = [ [ f ], [ g ] ]
Determinant: E = a*d
– b*c
If E ≠ 0, the solutions to the system Mx = S:
x1 = d/E * f – b/E * g
x2 = c/E * f + a/E * g
Memory Registers:
R0 = a
R1 = b
R2 = c
R3 = d
R4 = f
R5 = g
Hence [ [R0, R1], [R2, R3] ] * [ [x1], [x2] ] = [ [R4], [R5]
]. The determinant is stored in R6. Since so many storage registers are used, and
storage registers eat up programming memory, the program will need to be short.
Program:
CODE

STEP

KEY

COMMENT

13.0

00

RCL 0

Calculate det(M)

38

01

*


13.3

02

RCL 3


49

03




13.1

04

RCL 1


38

05

*


13.2

06

RCL 2


39

07

=


12.6

08

STO 6


13.3

09

RCL 3

Calculate x1

38

10

*


13.4

11

RCL 4


49

12




13.1

13

RCL 1


38

14

*


13.5

15

RCL 5


39

16

=


28

17

÷


13.6

18

RCL 6


39

19

=


51

20

R/S

Display x1

13.0

21

RCL 0

Calculate x2

38

22

*


13.5

23

RCL 5


49

24




13.2

25

RCL 2


38

26

*


13.4

27

RCL 4


39

28

=


28

29

÷


13.6

30

RCL 6


39

31

=


51

32

R/S

Display x2

Input:
Store values:
a [STO] 0, b [STO] 1, c [STO] 2, d [STO] 3; f [STO] 4, g
[STO] 5
Press [RST] [R/S]
If det(M) ≠ 0, x1 will be calculated. Press [R/S] to get x2.
Press [RCL] 6 to get the determinant of M.
Test: Solve
2*x1 + 3*x2 = 3.45
6*x1 + x2 = 4.26
R0 = 2, R1 = 3, R2 = 6, R3 = 1, R4 = 3.45, R5 = 4.26
Results: x1 =
0.4665, x2 = 1.461. Determinant = 20
(stored in R6)
TI65 Prime
Factorization
This prime factorization comes straight from the Texas
Instruments TI65 Manual.
Program:
CODE

STEP

KEY

COMMENT

12.1

00

STO 1

Store n in R1

0

01

0


12.0

02

STO 0

Store 0 for
comparisons

3

03

3


12.2

04

STO 2

Trail factor of 3

2^{nd} 53.0

05

LBL 0

Test 2 as a factor

13.1

06

RCL 1


28

07

÷


2

08

2


39

09

=


2^{nd} 28

10

FRAC

Is frac(R1/2)≠0?

3^{rd} 43

11

INV x=m

x≠m

0

12

0

R1≠R0?

2^{nd} 54.1

13

GTO 1

Go to odd factors

2

14

2


12.28

15

STO÷


1

16

1

STO÷ 1

51

17

R/S

Display 2 if it is
a factor

2^{nd} 54.0

18

GTO 0

GTO 0, test 2 again

2^{nd} 53.1

19

LBL 1

Odd factors loop
begins here

13.1

20

RCL 1


3^{rd} 42

21

INV x<m

x≥m

2

22

2

Is R1≥R2?

2^{nd} 54.2

23

GTO 2

All factors found?
No: GTO LBL 2

13.1

24

RCL 1

If complete,
display 1

51

25

R/S

(program execution
ends here)

2^{nd} 54.1

26

GTO 1


2^{nd} 53.2

27

LBL 2

Label 2 starts here

13.1

28

RCL 1


28

29

÷


13.2

30

RCL 2


39

31

=


2^{nd} 28

32

FRAC

Is frac(R1/R2)≠0?

3^{rd} 43

33

INV 3^{rd}
x=m

x≠m

0

34

0


2^{nd} 54.3

35

GTO 3


13.2

36

RCL 2

Display odd factor

51

37

R/S


12.28

38

STO÷


1

39

1

STO÷ 1

2^{nd} 54.1

40

GTO 1


2^{nd} 53.3

41

LBL 3

Test next odd
factor

2

42

2


12.59

43

STO+


2

44

2

STO+ 2

2^{nd} 54.1

45

GTO 1


Input: Enter n, press
[RST] [R/S]. Each prime factor is
displayed, keep on pressing [R/S] until you get 1 displayed.
Test 1: Factorize 102
Input: 102 [RST]
[R/S]
Result: 2, press [R/S]
Result: 3, press [R/S]
Result: 17, press [R/S]
Result: 1
Final result: 102 = 2
* 3 * 17
Test 2: Factorize 168
Input: 168 [RST] [R/S]
Repeated presses of [R/S] gives: 2, 2, 2, 3, 7, 1
Final result: 168 = 2
* 2 * 2 * 3 * 7 = 2^3 * 3 * 7
Resource: Texas
Instruments. “Texas Instruments
Professional TI65 Guidebook” 1986
This blog is property of Edward Shore, 2016.
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