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:
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CODE
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STEP
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KEY
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COMMENT
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38
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00
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*
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Start with f
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2
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01
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2
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38
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02
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*
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2nd 17
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03
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π
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39
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04
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=
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Calculate 2*π*f
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12.0
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05
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STO 0
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12.1
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06
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STO 1
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38
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07
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*
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51
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08
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R/S
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Prompt for L
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39
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09
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=
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12.0
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10
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STO 0
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Calculate XL
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13.1
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11
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RCL 1
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38
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12
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*
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51
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13
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R/S
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Prompt for C
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39
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14
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=
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34
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15
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1/x
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12.1
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16
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STO 1
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Calculate XC
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51
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17
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R/S
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Prompt for R
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12.2
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18
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STO 2
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2nd 33
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19
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x^2
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59
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20
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+
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16
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21
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(
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13.0
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22
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RCL 0
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49
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23
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-
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13.1
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24
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RCL 1
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17
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25
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)
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2nd 33
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26
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x^2
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39
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27
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=
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33
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28
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√
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-2nd 16
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29
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INV 2nd
ENG
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Remove ENG Notation
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51
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30
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R/S
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Display Z
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16
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31
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(
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13.0
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32
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RCL 0
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49
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33
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-
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13.1
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34
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RCL 1
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17
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35
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)
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28
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36
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÷
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13.2
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37
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RCL 2
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39
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38
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=
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-24
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39
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INV TAN
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arctangent
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51
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40
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R/S
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Display Φ
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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:
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CODE
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STEP
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KEY
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COMMENT
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13.0
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00
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RCL 0
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Calculate det(M)
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38
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01
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*
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13.3
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02
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RCL 3
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49
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03
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-
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13.1
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04
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RCL 1
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38
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05
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*
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13.2
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06
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RCL 2
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39
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07
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=
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12.6
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08
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STO 6
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13.3
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09
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RCL 3
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Calculate x1
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38
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10
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*
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13.4
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11
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RCL 4
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49
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12
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-
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13.1
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13
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RCL 1
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38
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14
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*
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13.5
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15
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RCL 5
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39
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16
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=
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28
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17
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÷
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13.6
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18
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RCL 6
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39
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19
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=
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51
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20
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R/S
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Display x1
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13.0
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21
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RCL 0
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Calculate x2
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38
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22
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*
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13.5
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23
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RCL 5
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49
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24
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-
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13.2
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25
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RCL 2
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38
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26
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*
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13.4
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27
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RCL 4
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39
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28
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=
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28
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29
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÷
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13.6
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30
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RCL 6
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39
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31
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=
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51
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32
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R/S
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Display x2
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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
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STEP
|
KEY
|
COMMENT
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12.1
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00
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STO 1
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Store n in R1
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0
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01
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0
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12.0
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02
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STO 0
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Store 0 for
comparisons
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3
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03
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3
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12.2
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04
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STO 2
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Trail factor of 3
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2nd 53.0
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05
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LBL 0
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Test 2 as a factor
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13.1
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06
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RCL 1
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28
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07
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÷
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2
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08
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2
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39
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09
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=
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2nd 28
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10
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FRAC
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Is frac(R1/2)≠0?
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-3rd 43
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11
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INV x=m
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x≠m
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0
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12
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0
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R1≠R0?
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2nd 54.1
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13
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GTO 1
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Go to odd factors
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2
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14
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2
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12.28
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15
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STO÷
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1
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16
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1
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STO÷ 1
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51
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17
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R/S
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Display 2 if it is
a factor
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2nd 54.0
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18
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GTO 0
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GTO 0, test 2 again
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2nd 53.1
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19
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LBL 1
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Odd factors loop
begins here
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13.1
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20
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RCL 1
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-3rd 42
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21
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INV x<m
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x≥m
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2
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22
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2
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Is R1≥R2?
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2nd 54.2
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23
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GTO 2
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All factors found?
No: GTO LBL 2
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13.1
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24
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RCL 1
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If complete,
display 1
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51
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25
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R/S
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(program execution
ends here)
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2nd 54.1
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26
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GTO 1
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2nd 53.2
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27
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LBL 2
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Label 2 starts here
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13.1
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28
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RCL 1
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28
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29
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÷
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13.2
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30
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RCL 2
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39
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31
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=
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2nd 28
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32
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FRAC
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Is frac(R1/R2)≠0?
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-3rd 43
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33
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INV 3rd
x=m
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x≠m
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0
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34
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0
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2nd 54.3
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35
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GTO 3
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13.2
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36
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RCL 2
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Display odd factor
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51
|
37
|
R/S
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12.28
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38
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STO÷
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1
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39
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1
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STO÷ 1
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2nd 54.1
|
40
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GTO 1
|
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2nd 53.3
|
41
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LBL 3
|
Test next odd
factor
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2
|
42
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2
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12.59
|
43
|
STO+
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2
|
44
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2
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STO+ 2
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2nd 54.1
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45
|
GTO 1
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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.