Wednesday, July 6, 2016

TI-55 III Programs Part II: Impedance of a Series RLC Circuit, Quadratic Equation, Error Function

TI-55 III Programs Part II: Impedance of a Series RLC Circuit, Quadratic Equation, Error Function

On to Part II!



TI-55 III:  Impedance of Series RLC Circuit

The impedance of a series RLC circuit in Ω (ohms) is:

Z = √(R^2 + (2*π*f*L – 1/(2*π*f*C))^2)

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:
Partitions allowed: 1-4
STEP
CODE
KEY
COMMENT
00
65
*
Start with f
01
02
2

02
65
*

03
91
π

04
95
=

05
61
STO

06
00
0
Store 2πf in R0
07
65
*

08
12
R/S
Prompt for L
09
75
-

10
53
(

11
71
RCL

12
00
0

13
65
*

14
12
R/S
Prompt for C
15
54
)

16
17
1/x

18
18
X^2

19
85
+

20
12
R/S
Prompt for R
21
18
X^2

22
95
=

23
13

24
41
INV

25
47
Eng
Cancel Eng Notation
26
12
R/S
Display Z

Input:  f [RST] [R/S], L [R/S], C [R/S], R [R/S]
Result:  Z

Test:
f = 60 Hz
L = 0.25 H
C = 16 * 10^-6 F
R = 150 Ω

Result:  166.18600 Ω

TI-55 III: Quadratic Equation

This program find the real roots of the equation:
X^2 + B*X + C = 0

Where:
D = B^2 – 4*C
If D ≥ 0, then continue the program since it will find the real roots.  Otherwise, stop since the roots are complex and is beyond the scope of this program.  The two roots are:
X1 = (-B + √D)/2
X2 = (-B - √D)/2

Program:
Partitions Allowed: 3
STEP
CODE
KEY
COMMENT
00
71
RCL
Calculate Discriminant
01
00
0

02
18
X^2

03
75
-

04
04
4

05
65
*

06
71
RCL

07
01
1

08
95
=

09
12
R/S
Display Discriminant
10
13

11
61
STO

12
02
2

13
75
-

14
71
RCL

15
00
0

16
95
=

17
55
÷

18
02
2

19
95
=

20
12
R/S
Display X1
21
53
(

22
71
RCL

23
00
0

24
85
+

25
71
RCL

26
02
2

27
54
)

28
94
+/-

29
55
÷

30
02
2

31
95
=

32
12
R/S
Display X2

Input:  B [STO] 0, C [STO] 1, [RST] [R/S]
Results:  Discriminant [R/S], root 1 [R/S], root 2

Test:  Solve X^2 + 0.05*X – 1 = 0
Input:  0.05 [STO] 0, 1 [+/-] [STO] 1 [RST] [R/S]
Results:  Discriminant = 4.0025  (It is non-negative, continue) [R/S]
X1 ≈ 0.9753125  [R/S]
X2 ≈ -1.0253125

TI-55 III: Gaussian Error Function

The error function is defined as:
erf(x) = ∫( 2*e^(-t^2)/√π dt, from t = 0 to t = x)

This program illustrates the integration function [ ∫ dx ] on the TI-55 III.

Program:
Prepare by pressing [2nd] [LRN] (Part) 3.  Integration needs a minimum of 3 memory registers.  That means, f(x) can take a maximum of 40 steps.
STEP
CODE
KEY
COMMENT
00
18
X^2
Integrand
01
94
+/-

02
41
INV

03
44
ln x
[INV] [ln x]: e^x (EXP)
04
65
*

05
02
2

06
55
÷

07
91
π

08
13

09
95
=

10
12
R/S

11
22
RST
End f(x) with =,R/S,RST

Input:  0 [STO] 1 (lower limit), x [STO] 2 (upper limit), [ ∫ dx ] n (number of partitions) [R/S]
Result: erf(x)
Test 1: erf(1.2) ≈ 0.910314. I use 12 partitions.
Input:  0 [STO] 1, 1.2 [STO] 2, [ ∫ dx ] 12 [ R/S ]
Result:  0.910314

Test 2:  erf(0.9) ≈ 0.7969082.   Store 0 in R0, 0.9 in R1.  12 partitions are used.

 Eddie

This blog is property of Edward Shore, 2016.



No comments:

Post a Comment

HP Prime and TI-84 Plus: Basic Wheatstone Full Bridge Circuit

HP Prime and TI-84 Plus:  Basic Wheatstone Full Bridge Circuit The program WHEATSTONE (HP Prime) and WHTSTONE (TI-84 Plus CE) deals wi...