Monday, July 4, 2016

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.

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”  2nd 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

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

This blog is property of Edward Shore, 2016.

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