TI-84 Plus CE and DM42: RLC Circuits

TI-84 Plus CE and DM42: RLC Circuits

The program RLC calculates:

(1) The total impedance across the entire circuit

(2) The phase angle, sometimes known as a power factor angle

(3) The total supply current

An RLC circuit is a circuit that connects one power supply to a resistor, an inductor, and a capacitor. The resistor, inductor, and capacitor can be connected in one of two ways: series or parallel. To calculate the total impedance (Z) and phase angle (θ), the rectangular to polar conversion function can be utilized.

In a general rectangular to polar conversion, (x, y) to (r, θ):

r = √(x^2 + y^2)

θ = arctan(y / x)

Formulas

Angular Frequency: ω = 2 * π * F	F = frequency in Hz V = supply voltage (volts) R = resistor in Ω (ohms) L = inductor in H (henrys) C = capacitance (farads) I = overall current (amps)
Series RLC Circuit - Formulas Z = √(R^2 + (ω*L – 1 / (ω*C))^2) θ = arctan ( (ω*L – 1 / (ω*C)) / R) I = V / Z	Series RLC Circuit – Set up for Rectangular to Polar Conversion x = ω*L – 1 / (ω*C) y = R Z = r
Parallel RLC Circuit - Formulas 1 / Z = √( (1/R)^2 + (1/(ω*L) – ω*C)^2) θ = arctan ( (1/(ω*L) – ω*C) / (1/R)) I = V / Z	Parallel RLC Circuit – Set up for Rectangular to Polar Conversion x = 1/(ω*L) – ω*C y = 1/R Z = 1/r

TI-84 Plus Program: RLC

ClrHome

Disp “RLC CIRCUIT”

Input “SUPPLY VOLTAGE? “, V

Input “FREQUENCY (HZ)? “, F

Input “RESISTANCE (OHMS)? “, R

Input “INDUCTOR (HENRYS)? “, L

Input “CAPACITOR (FARADS)? “, C

a+bi

Degree

2*π*F → W

Menu(“TYPE”, “SERIES”, 1, “PARALLEL”, 2)

Lbl 1

R+i*(W*L-1/(W*C)) → Z

abs(Z) → N

Goto 3

Lbl 2

(1/R)+i*(1/(W*L)-W*C) → Z

abs(Z)⁻¹ → N

Lbl 3

angle(Z) → θ

V/N → I

ClrHome

Disp “IMPEDANCE:”, N

Disp “PHASE ANGLE:”, θ

Disp “SUPPLY CURRENT:”, I

DM42, HP 42S Program: RLC

00 { 216-Byte Prgm }
01▸LBL "RLC"
02 "SUPPLY VOLTAGE?"
03 PROMPT
04 STO 01
05 "FREQUENCY?"
06 PROMPT
07 STO 02
08 "RESISTANCE?"
09 PROMPT
10 STO 03
11 "INDUCTOR?"
12 PROMPT
13 STO 04
14 "CAPACITOR?"
15 PROMPT
16 STO 05
17 DEG
18 2
19 STO 06
20 PI
21 STO× 06
22 RCL 02
23 STO× 06
24 "TYPE?"
25 AVIEW
26 PSE
27 "SERIES"
28 KEY 1 GTO 01
29 "PARA."
30 KEY 2 XEQ 02
31 MENU
32▸LBL 00
33 STOP
34 GTO 00
35▸LBL 01
36 CLMENU
37 EXITALL
38 RCL 06
39 RCL× 04
40 RCL 06
41 RCL× 05
42 1/X
43 -
44 RCL 03
45 →POL
46 STO 07
47 GTO 03
48▸LBL 02
49 CLMENU
50 EXITALL
51 RCL 06
52 RCL× 04
53 1/X
54 RCL 06
55 RCL× 05
56 -
57 RCL 03
58 1/X
59 →POL
60 1/X
61 STO 07
62▸LBL 03
63 "PHASE:"
64 AVIEW
65 PSE
66 VIEW ST Y
67 STOP
68 "IMPEADANCE:"
69 AVIEW
70 PSE
71 VIEW ST X
72 STOP
73 RCL 01
74 RCL÷ 07
75 "SUPPLY CURRENT:"
76 AVIEW
77 PSE
78 VIEW ST X
79 .END.

Examples

Examples are rounded to five digits.

Series Circuit

Inputs:

SUPPLY VOLTAGE: 300 V

FREQUENCY: 70 Hz

RESISTANCE: 80 Ω

INDUCTOR: 0.09 H

CAPACITOR: 150 μF (150E-6)

Results:

IMPEDANCE (Z) ≈ 83.64599 Ω

PHASE ANGLE (θ) ≈ 16.97904°

CURRENT (I) ≈ 3.58654 A

Parallel Circuit

Inputs:

SUPPLY VOLTAGE: 240 V

FREQUENCY: 90 Hz

RESISTANCE: 60 Ω

INDUCTOR: 20 mH (20E-3)

CAPACITOR: 140 μF (140E-6)

Results:

IMPEDANCE (Z) ≈ 52.46010 Ω

PHASE ANGLE (θ) ≈ 29.05363°

CURRENT (I) ≈ 4.57491 A

Sources

“Impedance and Complex Impedance” https://www.electronics-tutorials.ws/accircuits/impedance.html

“Parallel RLC Circuit Analysis” https://www.electronics-tutorials.ws/accircuits/parallel-circuit.html

“Series RLC Circuit Analysis” https://www.electronics-tutorials.ws/accircuits/series-circuit.html

Electronics Tutorials. AspenCore, Inc. 2024. Retrieved October 7, 2024 and October 17, 2024.

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Fun with the Texas Instruments TI-60

Fun with the Texas Instruments TI-60

Notes:

1.  I like to have the user input all the values into the registers before running the program.  This way, we can save program steps because the calculator doesn’t have to stop to ask for inputs.  Also, you don’t have to change all the values for different problems.  Finally, R/S can be used for only output.

2.  I keep register 0 (R0) out so that the user can have at least one register to store immediate results in further calculations.  I list the minimum partition for each program.

Great Circle Distance (in miles)

Formula:

D = acos (sin ϕ1 * sin ϕ2 + cos ϕ1 * cos ϕ2 * cos (λ1 – λ2)) * 3959 * π/180

Note: for kilometers, replace 3959 with 6371.

Where:

ϕ1, ϕ2:  Latitude of locations 1, 2; north is positive, south is negative

λ1, λ2:  Longitude of locations 1, 2:  east is positive, west is negative

Store before running:

R1:  ϕ1 as a decimal (convert from DMS if necessary)

R2:  λ1

R3: ϕ2

R4: λ2

Set the TI-60 in degrees mode.

Program (41 steps) – 2nd Part 5:

PG	OP	Key	PG	OP	Key
00	71	RCL	21	04	4
01	01	1	22	54	)
02	32	SIN	23	33	COS
03	65	*	24	95	=
04	71	RCL	25	12	INV
05	03	3	26	33	[COS]  (COS^-1)
06	32	SIN	27	65	*
07	85	+	28	03	3
08	71	RCL	29	09	9
09	01	1	30	05	5
10	33	COS	31	09	9
11	65	*	32	65	*
12	71	RCL	33	91	π
13	03	3	34	55	÷
14	33	COS	35	01	1
15	65	*	36	08	8
16	53	(	37	00	0
17	71	RCL	38	95	=
18	02	2	39	13	R/S
19	75	-	40	22	RST
20	71	RCL

Example:

Los Angeles:  ϕ = 34°13’ = 34.21666667°, λ = -(118°15’) = -(118.25°)

London:  ϕ = 51°30’26” = 51.50722222°, λ = -(0°7’39”) = -(0.1275°)

Result:  5431.617778 mi

Tip: For DMS-DD conversions: if you have a negative angle, enter the angle without the negative sign, do the conversion DMS-DD, then press [ +/- ].

Impedance of a Series Resonance Circuit

This program gives both the magnitude and phase angle. 

Impedance:   Z = R + j*(ω*L – 1/(ω*C))

Where:  ω = 2*π*F

Magnitude:  abs(Z)

Phase Angle:  arg(Z)

Variables:

R = resistance ( Ω )

C = capacitor ( farads )

L = inductor ( henrys )

F = Frequency (Hz)

Store before running:

R1:  R

R2:  C

R3:  L

R4:  F

Set the TI-60 in degrees mode.

Program (35 steps) – 2nd Part 5:

PG	OP	Key	PG	OP	Key
00	02	2	18	02	2
01	65	*	19	54	)
02	91	π	20	76	1/x
03	65	*	21	95	=
04	71	RCL	22	61	STO
05	04	4	23	05	5
06	95	=	24	71	RCL
07	61	STO	25	01	1
08	05	5	26	52	X<>Y
09	65	*	27	71	RCL
10	71	RCL	28	05	5
11	03	3	29	12	INV
12	75	-	30	38	[P-R] (R-P)
13	53	(	31	13	R/S
14	71	RCL	32	52	X<>Y
15	05	5	33	13	R/S
16	65	*	34	22	RST
17	71	RCL

Example:

Input:

R1:  R = 11.56 Ω

R2:  C = 0.0002 F

R3:  L =  0.018 H

R4:  F = 72 Hz

Results:

Phase Angle (θ) = -14.12679136°

Magnitude = 11.92049981

Linear Interpolation

Given points (x0, y0) and (x1, y1) with x0 < x < x1, we can estimate y by linear interpolation by:

y = ((x1 – x)*y0 + (x – x0)*y1)/(x1 – x0)

How good of an approximation depends on how close x0 and x1 are, and whether the curve that is being approximated is close to linear.

Store before running:

R1:  x1

R2:  y1

R3:  x2

R4:  y2

R5:  x

Program (34 steps) – 2nd Part 5:

PG	OP	Key	PG	OP	Key
00	53	(	17	01	1
01	53	(	18	54	)
02	71	RCL	19	65	*
03	03	3	20	71	RCL
04	75	-	21	04	4
05	71	RCL	22	54	)
06	05	5	23	55	÷
07	54	)	24	53	(
08	65	*	25	71	RCL
09	71	RCL	26	03	3
10	02	2	27	75	-
11	85	+	28	71	RCL
12	53	(	29	01	1
13	71	RCL	30	54	)
14	05	5	31	95	=
15	75	-	32	13	R/S
16	71	RCL	33	22	RST

Example:

Input:

R1:  x1 = 2

R2:  y1 = 3

R3:  x2 = 4

R4:  y2 = 8

R5:  x = 3

Result:

y = 5.5

Purchase of a Car:  How much can I afford?

The program will calculate the sticker price (price before sales tax) of an automobile that you can afford.  You give the term you want, the interest rate you qualify for, the sales tax rate, and the maximum payment you can afford.  This assumes that you don’t put any money down.

Formulas:

A = P/I * (1 – (1 + I)^-N) / (1 + S)

A = sticker price of the car

P = monthly payment

I = monthly interest rate of the loan, in decimal.   I = rate/1200

N = number of months.  N = years*12

S = sales tax rate, in decimal.  S = sales tax rate/100

Input:

R1:  number of payments

R2:  monthly interest rate

R3:  payment

R4:  sales tax rate, in decimal

Program (30 steps), 2nd Part 4:

PG	OP	Key	PG	OP	Key
00	71	RCL	15	45	y^x
01	03	3	16	71	RCL
02	55	÷	17	01	1
03	71	RCL	18	94	+/-
04	02	2	19	54	)
05	65	*	20	55	÷
06	53	(	21	53	(
07	01	1	22	01	1
08	75	-	23	85	+
09	53	(	24	71	RCL
10	01	1	25	04	4
11	85	+	26	54	)
12	71	RCL	27	95	=
13	02	2	28	13	R/S
14	54	)	29	22	RST

Example:

Input:

R1:  number of payments = 60, (5 year term)

R2:  monthly interest rate = 0.05/12 = 0.004166667, (5% annual interest rate)

R3:  payment = 400

R4:  sales tax rate, in decimal = 0.095, (9.5%)

Result:  19357.34

In this example, the highest sticker price that can be afforded is $19,357.34 (before sales tax).

I enjoy programming with the TI-60, unlike most Texas Instruments calculators that have keystroke programming, the TI-60 shows the step and key code you have entered instead of advancing to the next step with code 00. 

Eddie

This blog is property of Edward Shore, 2018.