## 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

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.