physics-class-12-unit-03-chapter-03-mobility-temperature-dependence-of-resistivity-current-l-3-11-4pjgtsilqku

### <Success style="font-size:25px"> Mobility Temperature Dependence Of Resistivity Current L-3 </Success>
### <primary style="font-size:24px"> Drift Velocity </primary>
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* Drift velocity $\vec{v}_d$

* $\vec{J}=-n e \vec{v}_\alpha$

* $\left|v_a\right|$ is small $\sim a$ few $\mathrm{mm} / \mathrm{s}$.

* $\vec{J}, \vec{E}$ Ohm's Law

- $\vec{J}=\sigma \vec{E}$

- $ \vec{E}=\rho \vec{J}$

- $\sigma=\text { Conductivily }$

- $\rho=\text { Resistivily }$

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<footer style = "font-size: 18px"> $\rightarrow$ Mobility and Temperature Dependence of Resistivity Current $\rightarrow$ <span style = "color:blue"> Drift Velocity </span> $\rightarrow$ Drift What is Resistance ? $\rightarrow$ Mobility </footer>

### <Success style="font-size:25px"> Mobility Temperature Dependence Of Resistivity Current L-3 </Success>
### <primary style="font-size:24px"> Drift What is Resistance ? </primary>
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- $R=\frac{\Delta V}{I} \quad \text { Ohms}$

- $R \propto$ Length

- $\propto \frac{1}{\text { Area of cross Section}}$

- 6. Microscopic view of Ohm's Law.

- $\tau$: Relaxation time

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

- $\tau \sim 10^{-14}$

- $ v_d=\frac{e E \tau}{m}$

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<footer style = "font-size: 18px">Mobility and Temperature Dependence of Resistivity Current $\rightarrow$ Drift Velocity $\rightarrow$ <span style = "color:blue"> Drift What is Resistance ? </span> $\rightarrow$ Mobility $\rightarrow$ Si at Room Temperature </footer>

### <Success style="font-size:25px"> Mobility Temperature Dependence Of Resistivity Current L-3 </Success>
### <primary style="font-size:24px"> Mobility </primary>
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- $R \propto {L}$
- $\propto \frac {1}{A}$

- Ease with which a charge carrier moves inside a solid when subjected to an electric field.

- $\mu = \frac{\left|v_d\right|}{|E|}=\frac{m / s}{v / m}  =\frac{m^2}{v-s} $

- $v_d=\frac{e E \tau}{m}$

- $\mu =  \frac{e \tau}{m} \sim \frac{10^{-19}+10^{-14}}{10^{-30}}$

- $\sim 10^{-3}$  to  $10^{-4} \mathrm{~m^2}/vs $

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<footer style = "font-size: 18px">Drift Velocity $\rightarrow$ Drift What is Resistance ? $\rightarrow$ <span style = "color:blue"> Mobility </span> $\rightarrow$ Si at Room Temperature $\rightarrow$ Ohm's Law </footer>

### <Success style="font-size:25px"> Mobility Temperature Dependence Of Resistivity Current L-3 </Success>
### <primary style="font-size:24px"> Si at Room Temperature </primary>
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| $1400 \mathrm{~cm}^2 / \mathrm{v-s }$ | electron mobility |
| -------- | -------- |
| $450 \mathrm{~cm}^2 / \mathrm{v-s}$    | hole mobility     |

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

- $\mu=\frac{e \tau}{m}$

- $ \sigma=e\left[n \mu_e+p \mu_n\right]$

- **Cu:**

- $n  =8.5 \times 10^{28} / \mathrm{m}^2$

- $\sigma  =5.8 \times 10^7 \mathrm{~s} / \mathrm{m}$

- $\mu=\frac{\sigma}{n e}  =\frac{5.8 \times 10^7}{8.5 \times 10^{28} \times 1.6 \times 10^{-19}}=0.0042 \mathrm{m}^2 / \mathrm{v}-\mathrm{s} =42 \mathrm{cm}^2 / \mathrm{v}-\mathrm{s}$

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<footer style = "font-size: 18px">Drift What is Resistance ? $\rightarrow$ Mobility $\rightarrow$ <span style = "color:blue"> Si at Room Temperature </span> $\rightarrow$ Ohm's Law $\rightarrow$ Break Down </footer>

### <Success style="font-size:25px"> Mobility Temperature Dependence Of Resistivity Current L-3 </Success>
### <primary style="font-size:24px"> Ohm's Law </primary>
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- $v_d  =\mu E $

- $E=10 \mathrm{V}$

- $ =4.3 \times 10^{-3} \times 10 $.

- $ = 4.2 \mathrm{~cm} / \mathrm{s}$

- Deviation from linearity - ohm's law.

- Does not depend on sign of $v$.

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<footer style = "font-size: 18px">Mobility $\rightarrow$ Si at Room Temperature $\rightarrow$ <span style = "color:blue"> Ohm's Law </span> $\rightarrow$ Break Down $\rightarrow$ Ohm's Law </footer>

### <Success style="font-size:25px"> Mobility Temperature Dependence Of Resistivity Current L-3 </Success>
### <primary style="font-size:24px"> Wire Bound and Carbon Resistance </primary>
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- **1.** Wire bound

- Alloys of manganin. constantine, Nichrome wires

- fraction of $\Omega$ to several hundred ohms.

- **2.** Carbon Resistance.
 
- Color coding

- Significant Figures

- multiplier

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<footer style = "font-size: 18px">Break Down $\rightarrow$ Ohm's Law $\rightarrow$ <span style = "color:blue"> Wire Bound and Carbon Resistance </span> $\rightarrow$ Wire Bound and Carbon Resistance Table $\rightarrow$ Wire Bound and Carbon Resistance Table </footer>

### <Success style="font-size:25px"> Mobility Temperature Dependence Of Resistivity Current L-3 </Success>
### <primary style="font-size:24px"> Wire Bound and Carbon Resistance Table </primary>
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| Color | Value |
| -------- | -------- |
| Black    | <span style="color:blue">0</span>     |
| Brown    | <span style="color:blue">1</span>     |
| Red      | <span style="color:blue">2</span>     |
| Orange   | <span style="color:blue">3</span>     |
| Yellow   | <span style="color:blue">4</span>     |
| Green    | <span style="color:blue">5</span>     |
| Blue     | <span style="color:blue">6</span>     |
| violet   | <span style="color:blue">7</span>     |
| Gray     | <span style="color:blue">8</span>     |
| white    | <span style="color:blue">9</span>     |

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<footer style = "font-size: 18px">Ohm's Law $\rightarrow$ Wire Bound and Carbon Resistance $\rightarrow$ <span style = "color:blue"> Wire Bound and Carbon Resistance Table </span> $\rightarrow$ Wire Bound and Carbon Resistance Table $\rightarrow$ Resistance </footer>

### <Success style="font-size:25px"> Mobility Temperature Dependence Of Resistivity Current L-3 </Success>
### <primary style="font-size:24px"> Resistance </primary>
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- B. B. Roy of Great Britain has a very Good Wife

- $ 47 \times 10^2 \pm$ 10 \%

- $=  4.7 \mathrm{k} \Omega \pm$ 10 \%

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<footer style = "font-size: 18px">Wire Bound and Carbon Resistance Table $\rightarrow$ Wire Bound and Carbon Resistance Table $\rightarrow$ <span style = "color:blue"> Resistance </span> $\rightarrow$ Thermal Expansion $\rightarrow$ Semiconductors </footer>

### <Success style="font-size:25px"> Mobility Temperature Dependence Of Resistivity Current L-3 </Success>
### <primary style="font-size:24px"> Thermal Expansion </primary>
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- **Resistance of a sample depends on temperature**

- Thermal Expansion $\Delta L=\alpha L \cdot \Delta t$

- $\rho-\rho_0= \rho_0 \alpha\left(T-T_0\right) $
 
 - $\rho=\rho_0\left[1+\alpha\left(T-T_0\right)\right] $
 
- $\alpha$ : Temperature coefficient

- $\alpha = \frac{1}{\rho_0} \frac{(\rho-\rho_0)}{T-T_0} $

- $ =\frac{1}{\rho_0} \frac{\Delta \rho}{\Delta t}$

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<footer style = "font-size: 18px">Wire Bound and Carbon Resistance Table $\rightarrow$ Resistance $\rightarrow$ <span style = "color:blue"> Thermal Expansion </span> $\rightarrow$ Semiconductors $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Mobility Temperature Dependence Of Resistivity Current L-3 </Success>
### <primary style="font-size:24px"> Semiconductors </primary>
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<footer style = "font-size: 18px">Resistance $\rightarrow$ Thermal Expansion $\rightarrow$ <span style = "color:blue"> Semiconductors </span> $\rightarrow$ Example $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Mobility Temperature Dependence Of Resistivity Current L-3 </Success>
### <primary style="font-size:24px"> Example </primary>
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- Al. 3 valence electrons.

- at $0^{\circ} \mathrm{C}$

- $\rho = 2.7 \times 10^{-8} \Omega \mathrm{~m}$.

- $\alpha=$ temperature coefficient = $ 4.3 \times 10^{-3} \mathrm{~K}^{-1}$

- calculate $\rho$ at Room Temp $25^{0} \mathrm{C}$

- $\rho_{25}  =\rho_0(1+\alpha . \Delta T) $

- $ =\rho_0\left(1+4.3 \times 10^{-3} \times 25\right)  =\rho_0(1.1) $

- $ =2.7 \times 1.1=2.97 \times 10^{-8} \Omega / \mathrm{m}$

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<footer style = "font-size: 18px">Thermal Expansion $\rightarrow$ Semiconductors $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Example $\rightarrow$ As T Incrases </footer>

### <Success style="font-size:25px"> Mobility Temperature Dependence Of Resistivity Current L-3 </Success>
### <primary style="font-size:24px"> Example </primary>
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- Al: Atomic mass 27.

- mass density $2700 \mathrm{~kg} / \mathrm{m}^3$

- $ \frac{2700}{27 \times 10^{-3}} \times 6 \times 10^{23} \approx 6 \times 10^{28} $

- $ n=1.8 \times 10^{29} / \mathrm{m}^3 $

-  electron density, $\sigma=\frac{n e^2 \tau}{m}$

- $ \tau \sim 7 \times 10^{-15} \mathrm{s}$, $ \mu=\frac{\sigma}{n e}=12 \mathrm{cm}^2 / \mathrm{v}-\mathrm{s}$

- $ \lambda=14.4 \mathrm{~nm}$

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<footer style = "font-size: 18px">Semiconductors $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ As T Incrases $\rightarrow$ Example </footer>