physics-class-12-unit-07-chapter-01-ac-current-generator-l-1-10-qklejz4ttxo

### <Success style="font-size:25px"> Ac Current Generator L-1 </Success>
### <primary style="font-size:24px"> Alternating Current Generator </primary>
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- According to Faraday's law of induction, $E=-\frac{d \Phi_B}{d }$

- Magnetic flux through a closed loop, ${\Phi}_B=\int \vec{B} \cdot d \vec{A}$

- $\vec{B}$ is uniform.

- $\Phi_B=\vec{B} \cdot \vec{A}=B . A \cos \theta$

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<footer style = "font-size: 18px"> $\rightarrow$ AC Current Generator $\rightarrow$ <span style = "color:blue"> Alternating Current Generator </span> $\rightarrow$ Alternating Current Generator $\rightarrow$ Alternating Current Generator </footer>

### <Success style="font-size:25px"> Ac Current Generator L-1 </Success>
### <primary style="font-size:24px"> Alternating Current Generator </primary>
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- The magnetic flux passing through loop is proportional to the magnetic field, depends on the area of the loop, and the angle between the area vector, and the magnetic field.

- Change in magnetic flux will induce any EMF.

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<footer style = "font-size: 18px">AC Current Generator $\rightarrow$ Alternating Current Generator $\rightarrow$ <span style = "color:blue"> Alternating Current Generator </span> $\rightarrow$ Alternating Current Generator $\rightarrow$ Induced Emf </footer>

### <Success style="font-size:25px"> Ac Current Generator L-1 </Success>
### <primary style="font-size:24px"> Alternating Current Generator </primary>
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- We can rotate the coil with respect to the magnetic field as a function of time.

- When the coil rotates, the area vector rotates, the rotation of the area vector implies that the change that is a change in angle

- The magnetic flux passing through loop changes with time and the changing magnetic flux will induce an EMF which will develop a potential difference across two points in the outside circuit.

- $\frac{d \Phi_B}{dt}<0$, $E>0$ and $\frac{d \Phi_B}{dt}>0$, $E<0$.

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<footer style = "font-size: 18px">Alternating Current Generator $\rightarrow$ Alternating Current Generator $\rightarrow$ <span style = "color:blue"> Alternating Current Generator </span> $\rightarrow$ Induced Emf $\rightarrow$ Generator </footer>

### <Success style="font-size:25px"> Ac Current Generator L-1 </Success>
### <primary style="font-size:24px"> Induced Emf </primary>
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- $\Phi_B=B.A \cos\theta$

- $\theta= \omega{t}$

- $\Phi_B=B.A\cos\omega t$

- Induced emf $E=-\frac{d\Phi_B}{dt}$

- $ = - \text{B A} \omega (-\sin\omega t)$

- $ = \text{B A} \omega \sin \omega t$

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<footer style = "font-size: 18px">Alternating Current Generator $\rightarrow$ Alternating Current Generator $\rightarrow$ <span style = "color:blue"> Induced Emf </span> $\rightarrow$ Generator $\rightarrow$ DC Generator </footer>

### <Success style="font-size:25px"> Ac Current Generator L-1 </Success>
### <primary style="font-size:24px"> DC Generator </primary>
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- DC generator works on the principle of electromagnetic induction.

- When a conductor is placed in a changing magnetic field, an electromotive force (EMF) is induced within the conductor.

- Using this principle you can convert a mechanical energy to electrical energy.

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<footer style = "font-size: 18px">Induced Emf $\rightarrow$ Generator $\rightarrow$ <span style = "color:blue"> DC Generator </span> $\rightarrow$ DC Generator $\rightarrow$ Displacement Current </footer>

### <Success style="font-size:25px"> Ac Current Generator L-1 </Success>
### <primary style="font-size:24px"> Displacement Current </primary>
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- There is a current which is changing as a function of time.

- You have a charge potential difference between these two plates there will be an electric field pointing between two plates.

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<footer style = "font-size: 18px">DC Generator $\rightarrow$ Displacement Current $\rightarrow$ <span style = "color:blue"> Displacement Current </span> $\rightarrow$ Electric Flux $\rightarrow$ Surface Charge Density </footer>

### <Success style="font-size:25px"> Ac Current Generator L-1 </Success>
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- $ \text{Current I} = \frac{dQ}{dt}$

- $ = {\epsilon_0}\frac{d\Phi_E}{dt}$

- $\Phi_E=\text{E A} = \frac{\sigma}{\epsilon_0}A=\frac{\theta}{\epsilon_0}$

- ${\sigma}$ : Surface Charge Density

- $\frac{d\Phi_E}{dt}=\frac{1}{\epsilon_0}\frac{dQ}{dt}$

- Current ${I_c}=\frac{dQ}{dt}$, Conduction Current.

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![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-07-chapter-01-ac-current-generator-l-1_10-qklejz4ttxo-p7.1.11.jpg)

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<footer style = "font-size: 18px">Displacement Current $\rightarrow$ Electric Flux $\rightarrow$ <span style = "color:blue"> Surface Charge Density </span> $\rightarrow$ Generalized Form of Ampere's Law $\rightarrow$ Modified Ampere's Law </footer>

### <Success style="font-size:25px"> Ac Current Generator L-1 </Success>
### <primary style="font-size:24px"> Example </primary>
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- Parallel plate capacitor

- Circular plates of radii r

- Capacitor getting charged

- $\oint \vec{B} \cdot \vec{dl}=\mu_0 \cdot I_c+\mu_0 ~\epsilon_0 \frac{d \Phi_E}{d t}$

- $=\mu_0 ~\epsilon_0 \frac{d \Phi_E}{d t}$
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<footer style = "font-size: 18px">Displacement Current Density $\rightarrow$ Flux $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Example $\rightarrow$ Example </footer>