TI-65 Programs Part III: Impedance and Phase Angle of a Series RLC Circuit, 2 x 2 Linear System Solution, Prime Factorization (from TI-65 Manual)

TI-65 Programs Part III:  Impedance and Phase Angle of a Series RLC Circuit, 2 x 2 Linear System Solution, Prime Factorization (from TI-65 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

TI-65 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	*
2nd 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
2nd 33	19	x^2
59	20	+
16	21	(
13.0	22	RCL 0
49	23	-
13.1	24	RCL 1
17	25	)
2nd 33	26	x^2
39	27	=
33	28	√
-2nd 16	29	INV 2nd 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

TI-65 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)

TI-65 Prime Factorization

This prime factorization comes straight from the Texas Instruments TI-65 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
2nd 53.0	05	LBL 0	Test 2 as a factor
13.1	06	RCL 1
28	07	÷
2	08	2
39	09	=
2nd 28	10	FRAC	Is frac(R1/2)≠0?
-3rd 43	11	INV x=m	x≠m
0	12	0	R1≠R0?
2nd 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
2nd 54.0	18	GTO 0	GTO 0, test 2 again
2nd 53.1	19	LBL 1	Odd factors loop begins here
13.1	20	RCL 1
-3rd 42	21	INV x<m	x≥m
2	22	2	Is R1≥R2?
2nd 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)
2nd 54.1	26	GTO 1
2nd 53.2	27	LBL 2	Label 2 starts here
13.1	28	RCL 1
28	29	÷
13.2	30	RCL 2
39	31	=
2nd 28	32	FRAC	Is frac(R1/R2)≠0?
-3rd 43	33	INV 3rd x=m	x≠m
0	34	0
2nd 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
2nd 54.1	40	GTO 1
2nd 53.3	41	LBL 3	Test next odd factor
2	42	2
12.59	43	STO+
2	44	2	STO+ 2
2nd 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 TI-65 Guidebook”  1986

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