Conductivity k, is equal to ………….
1) `1/R. l/A`
2) `G/A`
3) `Lambda_(m)`
4) `l/A`

Options

A. 1 & 2
B. 2 & 3
C. 3 &4
D. 1 & 4

Answer

To solve the question regarding the expression for conductivity (k), we will analyze the options provided and derive the correct relationship step by step.

### Step-by-Step Solution:

1. **Understanding Conductivity**:
- Conductivity (k) is a measure of a material's ability to conduct electric current. It is the reciprocal of resistivity (ρ).

2. **Relating Conductivity to Resistance**:
- The formula for resistivity (ρ) is given by:
\[ \rho = R \frac{A}{l} \]
where:
- \( R \) = resistance,
- \( A \) = cross-sectional area,
- \( l \) = length of the conductor.

3. **Finding Conductivity**:
- Since conductivity (k) is the reciprocal of resistivity, we can express it as:
\[ k = \frac{1}{\rho} \]

4. **Substituting the Expression for Resistivity**:
- Substituting the expression for resistivity into the equation for conductivity:
\[ k = \frac{1}{R \frac{A}{l}} = \frac{l}{R \cdot A} \]

5. **Identifying Conductance**:
- Conductance (G) is defined as:
\[ G = \frac{1}{R} \]
- Therefore, we can also express conductivity as:
\[ k = G \cdot \frac{1}{A} \]

6. **Analyzing the Options**:
- Now, let's analyze the options given in the question:
1) \( \frac{1}{R} \cdot \frac{l}{A} \)
2) \( \frac{G}{A} \)
3) \( \Lambda_m \) (molar conductance)
4) \( \frac{l}{A} \)

- From our derivation, we see that both option 1 and option 2 can represent conductivity:
- Option 1: \( \frac{1}{R} \cdot \frac{l}{A} \) is equivalent to \( k \).
- Option 2: \( \frac{G}{A} \) is also equivalent to \( k \).

7. **Conclusion**:
- Therefore, the correct answers are options 1 and 2.

### Final Answer:
- The conductivity \( k \) is equal to:
- 1) \( \frac{1}{R} \cdot \frac{l}{A} \)
- 2) \( \frac{G}{A} \)