ColumnI lists physical quantities for a uniform current carrying conductor . These quantities depend on quantities given in column II. Match entries in column I to all the quantities in column II on which it depends.
`{:(,"Column I",,"Column II"),((A),"Resistivity",(p),"Length of conductor"),((B),"Current through the conductor for a given potential difference across the condcutor",(q),"Electric field in conductor"),(( C),"Current density in condcutor for a given potential difference across the conductor ",(r ),"Temperature of conductor"),((D),"Thermal power generated per unit volume for given value of potential difference across the conductor",(s),"Nature of conductor"),(,,(t ),"Area of condcutor"):}`

Answer

To solve the problem of matching the physical quantities in Column I with the corresponding quantities in Column II, we will analyze each entry in Column I and determine which entries in Column II they depend on.

### Step-by-Step Solution:

1. **Identify the dependencies for Resistivity (A)**:
- Resistivity (ρ) is a property of the material and depends on:
- **Temperature (r)**: As temperature changes, the resistivity of a conductor changes.
- **Nature of conductor (s)**: Different materials have different resistivities.
- Therefore, for **A (Resistivity)**, the matches are **(r) Temperature** and **(s) Nature of conductor**.

2. **Identify the dependencies for Current through the conductor for a given potential difference (B)**:
- According to Ohm's Law, \( I = \frac{V}{R} \) and \( R = \frac{\rho L}{A} \). Thus, current depends on:
- **Length of conductor (p)**: As length increases, resistance increases, affecting current.
- **Area of conductor (t)**: As area increases, resistance decreases, affecting current.
- **Resistivity (r)**: Different materials (resistivity) will affect the current.
- **Temperature (r)**: Since resistivity changes with temperature, it indirectly affects current.
- Therefore, for **B (Current)**, the matches are **(p) Length of conductor**, **(t) Area of conductor**, **(r) Temperature**, and **(s) Nature of conductor**.

3. **Identify the dependencies for Current density in conductor for a given potential difference (C)**:
- Current density \( J = \frac{I}{A} \). From the previous analysis, we know:
- Current density is also dependent on:
- **Length of conductor (p)**: As length increases, it affects current density through resistance.
- **Resistivity (r)**: Current density is inversely related to resistivity.
- **Temperature (r)**: Since resistivity changes with temperature, it affects current density.
- **Nature of conductor (s)**: Different materials will have different current densities.
- Therefore, for **C (Current density)**, the matches are **(p) Length of conductor**, **(r) Temperature**, and **(s) Nature of conductor**.

4. **Identify the dependencies for Thermal power generated per unit volume for a given value of potential difference (D)**:
- The thermal power generated per unit volume can be expressed as \( P_{v} = \frac{I^2 R}{V} \). From our analysis:
- This depends on:
- **Length of conductor (p)**: As length increases, it affects the resistance and thus the power.
- **Resistivity (r)**: As resistivity increases, it affects the thermal power generated.
- **Temperature (r)**: Since resistivity changes with temperature, it affects thermal power.
- **Nature of conductor (s)**: Different materials will generate different amounts of thermal power.
- Therefore, for **D (Thermal power)**, the matches are **(p) Length of conductor**, **(r) Temperature**, and **(s) Nature of conductor**.

### Final Matches:
- **A (Resistivity)**: (r) Temperature, (s) Nature of conductor
- **B (Current)**: (p) Length of conductor, (t) Area of conductor, (r) Temperature, (s) Nature of conductor
- **C (Current density)**: (p) Length of conductor, (r) Temperature, (s) Nature of conductor
- **D (Thermal power)**: (p) Length of conductor, (r) Temperature, (s) Nature of conductor