physics-class-12-unit-03-chapter-02-drift-velocity-and-resistance-l-2-11-f2va70kb93w

### <Success style="font-size:25px"> Drift Velocity And Resistance L-2 </Success>
### <primary style="font-size:24px"> Example </primary>
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- No. of mols in $1 m^{3}$

- =$\frac {9 \times 10^3}{63.5 \times 10^{-3}}$
 
- No. of atoms =$\frac{9 \times 10^3}{63.5 \times 10^{-3}} \times 6.2 \times 10^{23}$.

- $\approx 8.5 \times 10^{28} m^{3}  \equiv n$

- $v_{\alpha} = \frac{J}{n e}$

- $= \frac{1.5 \times 10^{7}}{8.5 \times 10^{28} \times 1.6 \times 10^{-19}}$

- = $ 1.1 \times 10^{-3} m/s = 1.1 {mm} /{s}$ .

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<footer style = "font-size: 18px">Example $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Boltzmann constant $\rightarrow$ Ohm's Law </footer>

### <Success style="font-size:25px"> Drift Velocity And Resistance L-2 </Success>
### <primary style="font-size:24px"> Boltzmann constant </primary>
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- Average speed of electrons $\sim 10^6 m/s$

- Thermal speed of Cu atoms.

- $\frac{1}{2} m v_{t h}^2= \frac{3}{2} k_B T$

- $v_{t h} \approx \sqrt{\frac{K_Bt}{m}} $

- $K_B$ = Boltzmann constant

- $= 1.38 \times 10^-23. \frac {m^{2} kg}{s^2 K}$

- $ =\sqrt{\frac{1.38 \times 10^{-27} \times 300} { 63.5 \times 10^{-3}/ 6.2\times 10^{23}}}$

- $\approx 2 \times 10^{-2} m/s$

- $V_d << V_{th}$

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<footer style = "font-size: 18px">Example $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Boltzmann constant </span> $\rightarrow$ Ohm's Law $\rightarrow$ Ohm's Law </footer>

### <Success style="font-size:25px"> Drift Velocity And Resistance L-2 </Success>
### <primary style="font-size:24px"> Resistance Characterstics </primary>
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- $\rho=\frac{E}{J}  =\frac{\Delta V / L}{I / A} $

- $ =\left(\frac{\Delta V}{I}\right) \times \frac{A}{L} .$

- Resistance $R = \rho \times \frac{L}{A}$

- characterstics of a sample

- $R=\frac{\Delta V}{I}$

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<footer style = "font-size: 18px">Resistivity of Materials $\rightarrow$ Resistivity of Materials $\rightarrow$ <span style = "color:blue"> Resistance Characterstics </span> $\rightarrow$ Resistance of Copper $\rightarrow$ Charge Flow </footer>

### <Success style="font-size:25px"> Drift Velocity And Resistance L-2 </Success>
### <primary style="font-size:24px"> Resistance of Copper </primary>
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- Block of $\mathrm{Cu}$

- $1 cm \times 1cm \times 20cm$

- $R = \frac {\sigma L}{A} = \frac {1.3 \times 10^{-8} \times 20 \times 10^{-2}}{10^{-4}}$

- $=2.6 \times 10^{-5} \Omega$

- Resistance between rectangular ends.

- $R^{\prime}=\frac{1.3 \times 10^{-8} \times 10^{-2}}{20 \times 10^{-4}}=0.65 \times 10^{-7} \Omega$

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<footer style = "font-size: 18px">Resistivity of Materials $\rightarrow$ Resistance Characterstics $\rightarrow$ <span style = "color:blue"> Resistance of Copper </span> $\rightarrow$ Charge Flow $\rightarrow$ Charge Flow vs Heat Flow </footer>

### <Success style="font-size:25px"> Drift Velocity And Resistance L-2 </Success>
### <primary style="font-size:24px"> Charge Flow </primary>
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- $I =\frac{\Delta V}{R}=\frac{\Delta V}{\rho \cdot \Delta x / A}$

- $ =\sigma A \frac{\Delta V}{\Delta x} $

- $\frac{d Q}{d t}=-\sigma A \frac{d V}{d x}$

- Positive charges move in the x direction of decreasing potential.

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<footer style = "font-size: 18px">Resistance Characterstics $\rightarrow$ Resistance of Copper $\rightarrow$ <span style = "color:blue"> Charge Flow </span> $\rightarrow$ Charge Flow vs Heat Flow $\rightarrow$ Ohm's Law </footer>

### <Success style="font-size:25px"> Drift Velocity And Resistance L-2 </Success>
### <primary style="font-size:24px"> In the presence of $\vec{E}$ </primary>
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- $e^{-}$ are accelerated $\longrightarrow$ collide

- $\rightarrow$ emerge in random direction

- $\rightarrow$ collide

- $10^6 \mathrm{m} / \mathrm{s} \gg 10^{-3} \mathrm{m} / \mathrm{s}$

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<footer style = "font-size: 18px">Charge Flow vs Heat Flow $\rightarrow$ Ohm's Law $\rightarrow$ <span style = "color:blue"> In the presence of $\vec{E}$ </span> $\rightarrow$ Collision $\rightarrow$ Ohm's Law </footer>

### <Success style="font-size:25px"> Drift Velocity And Resistance L-2 </Success>
### <primary style="font-size:24px"> Collision </primary>
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- $a=\frac{e E}{m}$

- Time between two successive collision $=\tau \quad$

- Relaxation time

- $\vec{V}_i=$ velocity immediately after last Collision

- $\vec{V}_i =\vec{v}_i-\frac{e \vec{E}}{m} t $

- $ =\vec{v}_i-\frac{e \vec{E} \tau}{m}$

- $\left\langle\vec{v}_i\right\rangle=-\frac{e \vec{E}(\tau)}{m}$

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<footer style = "font-size: 18px">Ohm's Law $\rightarrow$ In the presence of $\vec{E}$ $\rightarrow$ <span style = "color:blue"> Collision </span> $\rightarrow$ Ohm's Law $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Drift Velocity And Resistance L-2 </Success>
### <primary style="font-size:24px"> Example </primary>
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- $v_{\mathrm{d}} \sim 1.1 \times 10^{-3} \mathrm{~m} / \mathrm{s}$

- $= \frac {eE}{m} .\tau$

- $\sigma=\frac{n e^2 \tau}{m}$ .

- $\rho =\frac{m} {ne^{2} \tau}$

- $1.7 \times 10^{-8}  =\frac{9 \times 10^{-31}}{8.5 \times 10^{28} \times 2.56 \times 10^{-38} \mathrm{\tau}}$

- $\tau  \approx 2.4 \times 10^{-14} \mathrm{~s}$

- **Mean Free path**

- $\lambda  =2.4 \times 10^{-14} \times 1.6 \times 10^6 $

- $ \approx 40 \mathrm{~nm}$

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<footer style = "font-size: 18px">Collision $\rightarrow$ Ohm's Law $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Thank You $\rightarrow$  </footer>