Consider the following quantities: number density of free electrons, n, mean free time of electrons between collisions,t , drift velocity of electrons, `v_d` , resistivity, p.
A constant potential difference is applied across a conductor. Assuming that the temperature of the conductor remains constant, which of these quantities is/are independent of the magnitude of the potential difference applied?

Options

A. n and p
B. `n, v_d and p`
C. n,t and p
D. only p

Explanation

To solve the question, we need to analyze each of the given quantities in relation to the applied potential difference across a conductor.

### Step-by-Step Solution:

1. **Understanding the Quantities:**
- **Number Density of Free Electrons (n):** This is the number of free electrons per unit volume in a material. It is a property of the material itself and does not change with the applied potential difference.
- **Mean Free Time (t):** This is the average time between collisions of the electrons. It is also a property of the material and is influenced by factors such as temperature, but not by the applied potential difference.
- **Drift Velocity (v_d):** This is the average velocity that a charged particle, such as an electron, attains due to an electric field. Drift velocity is directly proportional to the electric field (E), which is related to the applied potential difference (V) across the conductor. Therefore, v_d depends on the magnitude of the potential difference.
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