TI55 III Programs Part II: Impedance of a Series RLC
Circuit, Quadratic Equation, Error Function
On to Part II!
For Part I, click here: Digital Root, Complex Number Multiplication, Escape Velocity
For Part III, click here: Area and Eccentricity of Ellipses, Determinant and Inverse of 2x2 Matrices, Speed of Sound/Principal Frequency
TI55 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: 14
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
TI55 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 nonnegative,
continue) [R/S]
X1 ≈ 0.9753125
[R/S]
X2 ≈ 1.0253125
TI55 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 TI55 III.
Program:
Prepare by pressing [2^{nd}] [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.
This blog is property of Edward Shore, 2016.
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