Question

The graph between voltage \( V \) of a conductor and current \( I \) is a straight line, which makes an angle \( \theta \) with the y-axis (which represents \( I \)). The resistance of the conductor will be

• A. \( \tan \theta \)
• B. \( \cot \theta \)
• C. \( \sin \theta \)
• D. \( \cos \theta \)

Hint:

The slope of the \( V \)-\( I \) graph gives the resistance, which is \( \cot \theta \) when the angle \( \theta \) is measured with the horizontal axis.

Answer 1

The Correct Option is B

Step 1: Understanding the graph of \( V \) and \( I \).
The graph between voltage \( V \) and current \( I \) for a conductor is a straight line, and its slope represents the resistance of the conductor. The slope is given by the tangent of the angle \( \theta \) the graph makes with the horizontal axis (which is voltage).
Step 2: Applying the formula.
From Ohm's law, \( V = IR \), where \( R \) is the resistance. If the graph between \( V \) and \( I \) is a straight line, the slope \( \frac{V}{I} = R \). The angle \( \theta \) between the line and the horizontal axis gives the tangent of the angle as \( \tan \theta = \frac{V}{I} \). Therefore, the resistance is given by \( \cot \theta \).
Step 3: Conclusion.
Thus, the resistance of the conductor is \( \cot \theta \), which is the inverse of the tangent of the angle.
\[ \boxed{\text{Correct Answer: } \cot \theta} \]