Question

What does the slope of the V-I graph of a conductor represent?
A. capacitance
B. power
C. inductance
D. resistance

Answer 1

Hint: The slope of a graph can be found out using the derivative method. This means that the change in the variable in y-axis is divided by the change in variable at x-axis. Here the slope will be the change in velocity divided by the change in current. This may help you to solve this question.

Complete answer:
The ohm's law is the basic concept in order to solve this question.
Ohm's Law tells us that the current flowing in a circuit is found to be directly proportional to the potential difference which is applied and inversely proportional to the resistance of the circuit. However we can also say that by changing the voltage across a circuit twice, the current will also increase twice.
$R=\dfrac{V}{I}$
In order to solve this question, let us look at the graph showing the voltage and current.

Here the voltage has been represented in the y-axis and current in a conductor is expressed in the x-axis at constant temperature. This graph, the current $I$ against the potential difference $V$, is a straight line with fixed slope of $R$, since the relation is linear and also ohmic. By the way practical resistors sometimes show non-linear behaviour under particular conditions like the exposure to higher temperatures.
From this we can say that the slope of this graph will be the resistance of the circuit.

Note:
The resistance of a conductor is dependent on the area of the cross section of the conductor, the length of the conductor, and also its resistivity. It should be known that the electrical conductivity and resistivity are in inverse relation, which means that the more a material is conductive, then the less resistive it is.