The V-I graph for a good conductor makes angle `42 ^(@)` with V-axis. Here V denotes voltage and I denotes current. Then the resistance of the conductor will be

Options

A. `sin 42 ^(@)`
B. `cos 42 ^(@)`
C. `tan 42 ^(@)`
D. `cot 42 ^(@)`

Answer

To find the resistance of the conductor based on the given information about the V-I graph, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the V-I Graph**:
The V-I graph for a good conductor is linear, which means that the relationship between voltage (V) and current (I) is direct. The angle made with the V-axis is given as \(42^\circ\).

2. **Finding the Slope of the Graph**:
The slope (m) of the V-I graph is defined as the ratio of current (I) to voltage (V):
\[ m = \frac{I}{V} \]
The slope can also be expressed in terms of the angle \( \theta \) that the line makes with the V-axis:
\[ m = \tan(42^\circ) \]

3. **Using the Slope to Find Resistance**:
According to Ohm's Law, the resistance (R) is given by:
\[ R = \frac{V}{I} \]
We can rearrange the equation for the slope:
\[ \frac{I}{V} = \tan(42^\circ) \implies \frac{V}{I} = \frac{1}{\tan(42^\circ)} \]
Therefore, the resistance can be expressed as:
\[ R = \frac{1}{\tan(42^\circ)} \]

4. **Calculating the Resistance**:
To find the numerical value of the resistance, we need to calculate \( \tan(42^\circ) \). Using a calculator:
\[ \tan(42^\circ) \approx 0.9004 \]
Thus,
\[ R \approx \frac{1}{0.9004} \approx 1.11 \, \Omega \]

### Final Answer:
The resistance of the conductor is approximately \( 1.11 \, \Omega \).

---