The I-V graph for two different electrical appliances $P$ and $Q$ are shown in the figure in the diagram if $R_p$ and $R_q$ the resistances of the devices then :

A. \[{R_p} = {R_q}\]
B. \[{R_p} > {R_q}\]
C. \[{R_p} < {R_q}\]
D. None of these

Hint: To solve this question we will have to apply the basic knowledge about ohm’s law which gives the relationship between resistance (R), potential (V) and current (I). We will then equate the equation of ohm's law to the formula for the equation of straight line and then compare to answer the question.

Formula used:
Ohm’s law: \[V = IR\]
where, $V$= potential, $I$=current and $R$= resistance.

Complete step by step answer:
The link between electric current and potential difference is described by Ohm's law. The current flowing through most conductors is proportional to the voltage applied to them. We will use this law to answer this question. Ohm's law is only valid if the temperature and other physical variables remain constant.

Increasing the current in some components boosts the temperature. The filament of a light bulb is an example of this.. In this case, Ohm’s law cannot be applied. The light bulb filament violates Ohm’s Law. Now look at the formula \[V = IR\] if we equate it with \[x = ym\] we get that slope is given by $R$. Hence equation of graph becomes:
\[\dfrac{x}{m} = y\]
Hence as slope increases y decreases that is current decreases.Hence the correct answer would be \[{R_p} > {R_q}\].

Hence the correct answer is option B.

Note:In this question we equate the equation for ohm's law with the equation of the straight line, at that time remember that In this question , potential(V ) is placed on y-axis whereas current (I) is placed on x-axis. Do not exchange both the terms, or the answer would come out option C, which would be wrong.