In my opinion, every electrical (not electronical) consist mostly of just 5 possible components.
supplys: voltage source, current source
users: resistor (also wires), capacitor, spool.
Now every wire that is usually onsidered as a conductor is actually a resistor following Pouillet's law: the resistance of a conductor is directly proportional to its resistivity (a) and to its length (L) ; and is inversely proportional to this conductor section (S).
R = a x L/ S
R is the electrical resistance of the conductor in ohms
a is the matter resistivity in mm²/ m
L is the conductor length in m
S is the conductor section in mm²
Note: Depending on its diameter, the cable section is calculated as follow:
S=pi x d²/4
Depending on its radius, the cable section is calculated as follow:
S= pi x r²
Examples of a values in mm²/m at 20°C:
Copper 0.017
Silver 0.016
Alu 0.028
Iron 0.1
SO SHORT AND THICK WIRES GIVE THE LOWEST RESISTANCE!
When a current runs through a conductor, this conductor heats up. That’s what we call the joule effect.
This heat production is directly proportional to:
- The time during which the current goes through the conductor
- The square of the current intensity
- The resistance value
This is expressed by the following formula:
Q= R . I² . t Q in joules R in ohms I in amperes t in seconds
KNOWING THIS, IT'S BEST TO USE SHORT AND THICK WIRES BECAUSE THEY GIVE THE LOWEST RESISTANCE THUS LESS HEAT!
This in turn affects the resistance as explained by Mathiessen’s law, which can be expressed as follows:
Rt = R (1 + α t)
Rt is the resistance value at temperature t
R is the resistance value at 0°C
α is the conductor temperature coefficient
t is the temperature difference in centigrade degrees
Some α values:
- Copper, aluminium 0.004
- Tungsten 0.0065
- Silver 0.00377
- Bronze 0.0005
AND AGAIN THE SAME APPLYS
SO WHY MAKE THE EFFORT TO USE SHORT THICK WIRES?
WELL, IN THE END IT ALL COMES DOWN TO RESISTANCE!
TO PUT IT SIMPLE, IF A 100AMP CURRENT PASSES THROUGH A 0.01OHM WIRE U LOSE 1VOLT!
YOUR MOTOR IS THEN RUNNING ON JUST 7.4VOLTS.