Numerical Problems Based on Mobility of Charge Carriers for Class 12 Physics

Potential difference $V = 4.5\text{ V}$, length $l = 0.1\text{ m}$, drift velocity $v_d = 1.5 \times 10^{-4}\text{ ms}^{-1}$.

First, calculate the electric field ($E$) across the conductor:

Now, compute the electron mobility ($\mu$) using the relation $\mu = \frac{v_d}{E}$:

Given $n = 8.5 \times 10^{28}\text{ m}^{-3}$, Current $I = 1\text{ A}$, Length $l = 0.24\text{ m}$, Area $A = 1.2\text{ mm}^2 = 1.2 \times 10^{-6}\text{ m}^2$, Potential difference $V = 3\text{ V}$, and charge of electron $e = 1.6 \times 10^{-19}\text{ C}$.

1. Calculate the drift velocity ($v_d$):

2. Calculate the electric field ($E$):

3. Calculate electron mobility ($\mu$):

Electron mobility $\mu_e = 0.54\text{ m}^2\text{V}^{-1}\text{s}^{-1}$, Hole mobility $\mu_h = 0.18\text{ m}^2\text{V}^{-1}\text{s}^{-1}$.
Carrier density $n_i = n_e = n_h = 3.6 \times 10^{19}\text{ m}^{-3}$.
Elementary charge $e = 1.6 \times 10^{-19}\text{ C}$.

The total conductivity ($\sigma$) of an intrinsic semiconductor is the sum of the conductivities due to electrons and holes:

Substitute the given values:

Rounding to three decimal places: