The V-I graph for a good conductor makes angle `40^(@)` with V-axis. Here, V denotes voltage and I denotes current. The resistance of the conductor will be

Options

A. `sin 40^(@)`
B. `cos 40^(@)`
C. `tan 40^(@)`
D. `cot 40^(@)`

Explanation

To solve the problem, we need to find the resistance of the conductor given the angle of the V-I graph. Let's break it down step by step:

### Step 1: Understand the V-I Graph
The V-I graph represents the relationship between voltage (V) and current (I) for a conductor. The slope of the line in this graph is related to the resistance of the conductor.

### Step 2: Identify the Angle
The problem states that the angle between the V-axis and the line representing the conductor is \(40^\circ\).

### Step 3: Relate the Angle to the Slope
The slope (m) of the V-I graph can be expressed in terms of the angle \(\theta\) as:
\[ m = \tan(\theta) \]
In this case, \(\theta = 40^\circ\), so:
\[ m = \tan(40^\circ) \]

### Step 4: Use Ohm's Law
According to Ohm's Law, the resistance \(R\) can be defined as:
\[ R = \frac{V}{I} \]
From the slope of the V-I graph, we can also express it as:
\[ m = \frac{V}{I} \]
Thus, we can equate the two expressions:
\[ R = \frac{1}{m} \]

### Step 5: Substitute the Slope
Substituting the slope we found earlier:
\[ R = \frac{1}{\tan(40^\circ)} \]

### Step 6: Simplify Using Cotangent
Using the identity that \(\cot(\theta) = \frac{1}{\tan(\theta)}\):
\[ R = \cot(40^\circ) \]

### Final Result
Thus, the resistance of the conductor is:
\[ R = \cot(40^\circ) \]