Question

The current-voltage graph for a device is shown in figure. The resistance is negative in region:

(a) AB
(b) BC
(c) ABC
(d) None of these

Answer 1

Hint: Resistance is given as $R={\displaystyle \frac{V}{I}}$. Here the slope gives us the value $m={\displaystyle \frac{\mathrm{\Delta }I}{\mathrm{\Delta }V}}={\displaystyle \frac{I_2-I_1}{V_2-V_1}}$which is nothing but $m={\displaystyle \frac{1}{R}}$. Therefore, try to figure for which part the slope will be negative.

Complete step by step answer:
From Ohm’s Law we have,
$$\begin{gathered} V=IR \\ \Rightarrow R={\displaystyle \frac{V}{I}} \end{gathered}$$
And the graph is I vs V so the slope will be,
$m={\displaystyle \frac{\mathrm{\Delta }I}{\mathrm{\Delta }V}}={\displaystyle \frac{I_2-I_1}{V_2-V_1}}$
On further simplification,
$$R={\displaystyle \frac{1}{m}}$$
Now from the graph we see that for part AB the slope is negative, for point B slope is zero and for part BC the slope is positive. Therefore, the part for which the resistance is negative is AB.
The correct answer is option A.

Note:Be careful in evaluating the slope. Read the axes carefully whether V is on x-axis or y-axis. Many times students evaluate slope m=R=V/I in a hurry. Well the answer remains the same and correct in case of multiple choice. But in case of subjective questions, marks will be deducted.