"The amount of current flowing in a circuit made up of pure resistances is directly proportional to the electromotive forces impressed on the circuit and inversely proportional to the total resistance of the circuit."

In simpler terms:

A steady increase in voltage, in a circuit with constant resistance,
produces a constant rise in current.

A steady increase in resistance, in a circuit with constant voltage,
produces a progressively weaker current.

The quote above is an extremely important quote. Remember, everything in a circuit has resistance. And this is the basis of Ohm's Law, the basic fundemental building block of electronics.

If you are going to repair electronics, you may never need them. But if you want to know how it works, design circuits, even find the proper resistance to supply the proper voltage to a lamp or LED. Learn Ohm's Law -- Learn it inside and out!

**Resistance** is anything that causes an opposition to the flow of electricity
in a circuit. It is measured in Ohmic resistance, its unit of measure is
the **Ohm**. The symbol is [Greek Letter omega or R].

If we look at our garden hose as a peice of wire the size of the hose would determine the resistance. If we were to step on our rubber garden hose we could create a resistor. The harder we step, the greater the resistance. And if we step hard enough to stop the flow of water, we reach infinity or open circuit, electrons/water simply stop flowing.

**Intensity** is the current or flow of electrons through the circuit. **Current**
is measured in **Amperes**, and the unit of measure is the **Amp**. The symbol is
[I or A]. Back to our garden hose. With the pressure the same, the size of
the hose determines the intensity. Again step on the hose, increase the
resistance, beyound the point of resistance, we reduce the intensity, PSI
and GPM drops.

**Power** is the energy dissipated in an electronic circuit or component. Power
is measured in **Wattage**, and the unit of measure is the **Watt**. The symbol is
[P or W]. We can look at Power as the rate of doing work, with our garden
hose this would be the gallons per minute [GPM].

Now lets see if we can put all this to work in a simple DC circuit.

Based on Ohm's Law

E = I * R

I = E / R

R = E / I

P = E * I.

It is proven by the fact that 1 Volt across a resistance of 1 Ohm has 1 Amp
of current through it. And dissipates 1 Watt of power.

If we have a power source with a resistive load of 1 Ohm, that has a Current
of 12 Amps. We know that Voltage = 12 Amps * 1 Ohm = 12 Volts. [E=I*R]
If we have a 12 Volt source and a resistive load of 1 Ohm, we know that
Intensity [Current] = 12 Volts / 1 Ohm = 12 Amps. [I=E/R].
If we have a 12 Volt source, and the current being generated is 12 Amps, we
know Resistance = 12 Volts / 12 Amps = 1 Ohm. [R=E/I] We also know Power =
12 Volts * 12 Amps = 144 Watts of energy is being dissipated by our 1 Ohm
load. [P=E*I].

Now you can play with any of the above examples, and see how it works for yourself. Even get out the garden hose and play with it to get an idea of how each relate to the other.

Keep in mind, when we look at a ballast resistor, or more properly named/defined as a current limiting resistor, we are concerned with all the building blocks, the [V]oltage across it in Volts, the [I]ntensity through it in Amps, and the [P]ower it has to dissipate in Watts.

Using a 12Vdc power source to power a 1.5V 25mA lamp as an example:

Now we know we have 12Vdc and we only want the lamp to see 1.5Vdc, so we know we have to drop 12-1.5 = 10.5Vdc. We have multiple ways to do this: Voltage regulation, Current regulation, Diode voltage drops, or a current limiting resistor. Since we are talking resistors here, lets go with this method. We know we have to drop 10.5Vdc, and we know we do not want the lamp to receive more then 25mA at 1.5Vdc. We go back to Ohm's Law to find out what resistance value we need for this. Or simply what value in Ohms will drop 10.5Vdc at a current of 25mA. Ohm's law says [R]esistance = [E]mf / [I]ntensity in Amps. Or if you like, Voltage drop across / Current through = Ohmic Resistance. So we take 10.5V / 0.025A = 420 Ohms. We also need to know how hard this resistor has to work, again Ohm's Law says [P]ower in Watts = E*I or 10.5 times 0.025 = 0.262 Watts.

I hope by now we can see, we are dropping the Voltage by limiting the Current through a resistor. Change any one value, and the results will be different.

FYI:

Voltage Regulation means regardless of load in Amp [within specs] the
Voltage will remain the same.

Current Regulation means regardless of Voltage [within specs] the Current
will remain the same.

Ballast or Current limiting resistor means no regulation at all, Change any
one value, and the results will be different.