dc-electricity 0.2.9

An educational package about linear DC electrical circuits

dcelectricity package

The aim of this project is to understand the rudiments of DC electrical circuits and their functioning (primary and secondary school curricula).

Prerequisites

Python : version 3
All operating systems

Installing dcelectricity python package

From Pypi repository :
https://pypi.org/project/dc-electricity

pip install dc-electricity

Basic electrical quantities

• Voltage (volt)
• Current (ampere)
• Resistance (ohm)
• Conductance (siemens)
• Power (watt)
• Energy (joule / kWh)

Electrical laws

• Kirchhoff’s current law
• Kirchhoff’s voltage law
• Ohm's law
• Resistors in series and parallel
• Voltage divider and current divider
• Millman's theorem
• Joule's first law (P=I²R=V²/R)
• Power law (P=VI)
• Energy formula (P=E/t)

DC Circuit diagram

Circuit should only contain :

• independent voltage source
• independent current source
• resistors

A complete example

            V1
        <---------
         +------+
   --->--| R1   |--------+-------+
     I1  +------+        |       |
 ^                    I2 v       v I3
 |                       |       |      ^
 |                     +---+   +---+    |
 |                     |   |   |   |    |
E|                     |R2 |   |R3 |    | V2
 |                     |   |   |   |    |
 |                     +---+   +---+    |
 |                       |       |
                         |       |
   ----------------------+-------+

Datas :
E = 12 V ; R1 = 1 kΩ ; R2 = 2.7 kΩ ; R3 = 1.8 kΩ
What are the I1, I2, I3 currents ?
What are the V1, V2 voltages ?

>>> from dcelectricity.dc_en import *  # english version
>>> # from dcelectricity.dc_fr import *  # french version
>>> E = Voltage(12)
>>> E
Voltage : 12.000000 V
>>> R1 = Resistor(1, 'k')
>>> R1
Resistance : 1000 Ω (1.000000 kΩ)
>>> R2 = Resistor(2.7, 'k')
>>> R3 = Resistor(1.8, 'k')
>>> R23 = R2//R3  # resistances in parallel
>>> R23
Resistance : 1080 Ω (1.080000 kΩ)
>>> Req = R1 + R23  # resistances in series
>>> Req
Resistance : 2080 Ω (2.080000 kΩ)
>>> I1 = E/Req  # Ohm's law
>>> I1
Current : 0.00576923 A (5.769231 mA)
>>> V1 = I1*R1  # Ohm's law
>>> V1
Voltage : 5.769231 V
>>> V2 = E - V1  # Kirchhoff’s voltage law
>>> V2
Voltage : 6.230769 V
>>> I2 = V2/R2  # Ohm's law
>>> I2
Current : 0.00230769 A (2.307692 mA)
>>> I3 = I1 - I2  # Kirchhoff’s current law
>>> I3
Current : 0.00346154 A (3.461538 mA)

Resistances and conductances

>>> G2 = 1/R2
>>> G2
Conductance : 0.00037037 S (370.370370 µS)
>>> G3 = 1/R3
>>> 1/(G2+G3)
Resistance : 1080 Ω (1.080000 kΩ)
>>> R2*(R3/(R2+R3))
Resistance : 1080 Ω (1.080000 kΩ)
>>> 1/(1/R2 + 1/R3)
Resistance : 1080 Ω (1.080000 kΩ)

Law class

>>> law = Law()
>>> # voltage divider
>>> V2 = law.VoltageDivider(vtotal=E, r=R2//R3, r2=R1)
>>> V2
Voltage : 6.230769 V
>>> # Millman's theorem
>>> gnd = Voltage(0)
>>> V2 = law.Millman(v_r=[(E, R1), (gnd, R2), (gnd, R3)])
>>> V2
Voltage : 6.230769 V
>>> (E/R1)/(1/R1 + 1/R2 + 1/R3)
Voltage : 6.230769 V
>>> V2/E
0.5192307692307693
>>> # current divider
>>> I3 = law.CurrentDivider(itotal=I1, r=R3, r2=R2)
>>> I3
Current : 0.00346154 A (3.461538 mA)
>>> I1*R2/(R2+R3)
Current : 0.00346154 A (3.461538 mA)

Electrical power, Joule's first law

>>> P = E*I1  # source power
>>> P
Power : 0.0692308 W (69.230769 mW)
>>> P1 = law.Joule(r=R1, i=I1)
>>> P1
Power : 0.033284 W (33.284024 mW)
>>> R1*I1*I1
Power : 0.033284 W (33.284024 mW)
>>> law.Joule(r=R1, v=V1)
Power : 0.033284 W (33.284024 mW)
>>> V1*(V1/R1)
Power : 0.033284 W (33.284024 mW)
>>> P2 = law.Joule(r=R2, i=I2)
>>> P2
Power : 0.0143787 W (14.378698 mW)
>>> P3 = law.Joule(r=R3, i=I3)
Power : 0.021568 W (21.568047 mW)
>>> P1+P2+P3
Power : 0.0692308 W (69.230769 mW)

Energy and power

>>> T = Time(1800)  # or T = Time(0.5, 'h')
>>> P = Power(1500)
>>> E = P*T  # or E = law.Energy(t=T, p=P)
>>> E
Energy : 2.7e+06 J (2.700000 MJ) 0.75 kWh
>>> E/P
Time : 1800 s (1.800000 ks) 0.5 h
>>> E/T
Power : 1500 W (1.500000 kW)

Advantages and limitations

This module manages basic arithmetic operations + - * / as well as // which designates two resistors in parallel.

The dimensional homogeneity is checked :

>>> V3 = V1 - V2 + I3  # V+A -> Error
TypeError
>>> I = I1 + 0.5  # A+number -> Error
TypeError
>>> I2 = Current(0.5)
>>> I = I1 + I2
>>> I = 5*I2 - V1/R1 + I3

The result of an operation must give a quantity whose unit is one of : V, A, Ω, S, W, J, s, no unit (ratio).
Otherwise, you will get an error :

>>> R1/V1  # Ω/V -> 1/A -> Error
TypeError
>>> R2*(R3/(R2+R3))  # Ω*(Ω/Ω) -> Ω*() -> Ω
>>> R2*R3/(R2+R3)  # Ω*Ω -> Error
TypeError
>>> P = V1*(V1/R1)  # V*(V/Ω) -> V*A -> W
>>> P = V1*V1/R1    # V*V -> Error
TypeError
>>> V1()**2/R1()

See also

http://fsincere.free.fr/isn/python/cours_python_dc.php

https://pypi.org/project/ac-electricity