1)
What is a characteristic curve ?
Definition: A characteristic curve is the graph on which are
represented the variations in the voltage at the terminals of a
component as a function of the current passing through it.

2)
How to draw the characteristic curve of a resistor ?
To draw the characteristic curve of resistor we need the following
circuit:

This circuit consists of a battery providing a variable voltage, a
resistor, an ammeter and a voltmeter.

If the voltage of the battery changes there is a variation of voltage
for the resistor and also a variation of electric current.

The measuring instruments are used to determine several couples of
values (voltage and current).

These couples are the coordinates of points used to draw the
characteristic curve on a graph with the current on abscissa
axis(horizontal axis) and the voltage on ordinate axis (vertical axis).

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3)
Properties of the characteristic curve of a resistor
The characteristic curve of a resistor is always a line passing through
the origin point.

This line indicates that the voltage of the resistor is proportional to
the current.

The proportionality coefficient corresponds to the resistance.

example:

For a 10 ohm resistor we obtain, thanks to the measures, the following
points:

(I = 0.1 A, U = 1 V), (I = 0.2 A, U = 2 V), (I = 0.3 A, U = 3 V)

(I = 0.4 A, U = 4 V) etc.

These values are used to draw the following graph:

The voltage is ten time greater than current: ten is also the
resistance.

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