Say you want to measure voltage between two points in a circuit. If the meter resistance is too low, it provides an alternative current path to those in the circuit itself. That changes the flow of current and changes the voltage pattern. In effect, it partly shorts out the circuit, reducing the voltage.
If you have a conductor with a fixed total current, then the more area the current flows through, the less current flows per unit area. That means that the charge carriers are flowing more slowly. For very small areas, in some circuits the voltage is nearly constant and the current just goes up as the area increases. For large enough areas, the circuit's ability to supply current will be too limited, and the voltage will drop, as described above.
Incandescent lamps are usually powered by a fixed-voltage source. If the resistance R is high, the power V2
/R will be low. The light power out will always be less than the electrical power in, so high R means low light output.
(published on 06/03/2011)