Imagine, for a minute that electricity travels quite slowly.
When you turn your light switch on what happens? Current starts to flow - it starts working its way down the wire and so does the voltage. The current that flows is determined by two things: -
- The voltage and
- An "impression" of what the load resistance might be.
Will the current be too small or will the current be too much? It is the cable (and its properties) that dictate the amount of current flowing.
Voltage and current are traveling to the "unknown" load and because V and I are flowing there is power flowing (P = VI). When the current and voltage reach the bulb, if the bulb's resistance doesn't match the V/I relationship not all the power is consumed.
This means the excess (or deficit) of power has to be reflected back up the wire to the switch. It's got nowhere else to go.
In the real world of data comms or radio, this causes "reflections" and these can add or subtract to the forward power traveling down the wire and, in the case of data, it can become misshaped leading to possible data corruptions. In the case of an RF carrier, there will be points along the wire where it appears unmeasurable.
The cable dictates how much current initially flows based (mainly) on its inductance, capacitance and resistance. The formula is this: -
Characteristic impedance = \$\sqrt{\dfrac{R+j\omega L}{G+j\omega C}}\$
R is resistance per metre, L is inductance per metre, C is parallel capacitance per metre and G is parallel conductance per metre. At high frequencies (>1MHz) the impedance starts to largely become: -
\$\sqrt{\dfrac{L}{C}}\$ and if you look at some coax specs you'll see that 50 ohms is the result of this calculation.
why can't I use a 75 ohm in place of a 50 ohm on the output of my
transmitter?
Hopefully, by now you should be able to answer this.
Best Answer
The equation which answers your questions is that of the characteristic impedance of the transmission line, which arises from both inductance and capacitance: $$Z_0=\sqrt{\frac{R+j\omega L}{G+j\omega C}}$$
For a lossless transmission line this is simply: $$ Z_0 = \sqrt{\frac{L}{C}} $$
You should also check out the Telegrapher's Equations. They are one of the first steps in to transmission lines, a scary and wonderful topic.