physics-class-12-unit-07-chapter-09-lc-oscillations-l-9-10-05ak6ujmrki

### <Success style="font-size:25px"> Lc Oscillations L-9 </Success>
### <primary style="font-size:24px"> Spring Mass </primary>
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- $F=-Kx$

- $m\frac{d^2x}{dt^2}=-Kx$

- $x=x_0 \cos (\omega t),$ where

- $\omega=\sqrt{\frac{x}{m}}$

- Since at t = 0

- $x=x_0$

- Spring mass system executes SHM

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<footer style = "font-size: 18px">Spring Energy $\rightarrow$ Spring Energy $\rightarrow$ <span style = "color:blue"> Spring Mass </span> $\rightarrow$ LC-Oscillation $\rightarrow$ Magnetic Energy </footer>

### <Success style="font-size:25px"> Lc Oscillations L-9 </Success>
### <primary style="font-size:24px"> LC-Oscillation </primary>
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- 1 - 2 connected capacitor will be charged at t = 0 $Q=Q_{max}$ I = 0

- Disconnected 1 - 2 but Connect 1 - 3

- Currenr flows $\frac{dI}{dt}>0$

- $I=-\frac{dQ}{dt}$

- $-L\frac{dI}{dt}+\frac{Q}{C}=0$

- $\frac{d^2 x}{dt}+\frac{Q}{LC}=0 \Leftrightarrow \frac{d^2x}{dt^2}+\frac{k}{m}x=0$

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<footer style = "font-size: 18px">Spring Energy $\rightarrow$ Spring Mass $\rightarrow$ <span style = "color:blue"> LC-Oscillation </span> $\rightarrow$ Magnetic Energy $\rightarrow$ Energy density </footer>

<h3 id="success-stylefont-size25px-lc-oscillations-l-9-success-2"><Success style="font-size:25px"> Lc Oscillations L-9 </Success></h3>
<h3 id="primary-stylefont-size24px-kinetic-energy-primary"><primary style="font-size:24px"> Kinetic energy </primary></h3>
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<p>Kinetic energy of spring mass</p>
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<p>$\leftrightarrow$ magnetic energy (L - C)</p>
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<p>$\frac{1}{2}mv^2 \leftrightarrow \frac{1}{2}LI^2$</p>
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<p>$v \leftrightarrow I$, $x \leftrightarrow Q$, $m \leftrightarrow L$</p>
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<p>$\frac{1}{2}kx^2 \leftrightarrow \frac{Q^2}{2C}$</p>
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<p>$k \leftrightarrow \frac{1}{C}$</p>
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<p>Total mechanical energy</p>
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<p>$P.E. + x.E \Leftrightarrow U_E + U_B =$ Electromaganetic</p>
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<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-07-chapter-09-lc-oscillations-l-9_10-05ak6ujmrki-200-2383.2.jpg"></p>
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<footer style = "font-size: 18px">Magnetic Energy $\rightarrow$ Energy density $\rightarrow$ <span style = "color:blue"> Kinetic energy </span> $\rightarrow$ Example $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Lc Oscillations L-9 </Success>
### <primary style="font-size:24px"> Example </primary>
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- L = 50 mH, C = 20 $\mu F$

- Inactually current is maximum How long does it take to fully charge the capacitor?

- $\omega =\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{5 \times 10^{-2} \times 2 \times 10^{-5}}}$

- $=10^{2} rad/s$

- $T=\frac{2 \pi}{\omega}=6.3 ms$

- $T/4 \cong 1.6 ms$

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<footer style = "font-size: 18px">Energy density $\rightarrow$ Kinetic energy $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Example $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Lc Oscillations L-9 </Success>
### <primary style="font-size:24px"> Properties </primary>
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- 1. Considered LC circuit

- 2. Charge and current oscillation

- $\omega=\frac{1}{\sqrt{LC}}$

- 3. Established a parallel between L-c circuit and a mechanical circuit

- $Q \leftrightarrow x$, $I \leftrightarrow v$, $L \leftrightarrow m$, $c \leftrightarrow 1/x$

- electrical $\leftrightarrow$ spring energy

- magnetic $\leftrightarrow$ kinetic energy
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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-09-lc-oscillations-l-9_10-05ak6ujmrki-279-3428.4.jpg)

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<footer style = "font-size: 18px">Example $\rightarrow$ Maximum energy $\rightarrow$ <span style = "color:blue"> Properties </span> $\rightarrow$ Thank You $\rightarrow$  </footer>