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!

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

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 [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.

 Eddie

This blog is property of Edward Shore, 2016.