physics-class-12-unit-07-chapter-04-capacitive-circuits-alternating-currents-l-4-10-i67tl-hqxgm

### <Success style="font-size:25px"> Capacitive Circuits Alternating Currents L-4 </Success>
### <primary style="font-size:24px"> Alternating Current/Voltages </primary>
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- $I=\frac{V_m}{R} \sin \omega t$

- $=Im \sin \omega t$

- Currrent is in-phase with voltage.

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<footer style = "font-size: 18px"> $\rightarrow$ Capacitive Circuits Alternating Current $\rightarrow$ <span style = "color:blue"> Alternating Current/Voltages </span> $\rightarrow$ Phaser (Resistive cct) $\rightarrow$ Pure Inductive Circuit </footer>

### <Success style="font-size:25px"> Capacitive Circuits Alternating Currents L-4 </Success>
### <primary style="font-size:24px"> Pure Inductive Circuit </primary>
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- $< I > = 0$ Over cycle

- $P_ {av} = \frac{I_ {m}^2R}{2}=I_{rms}^2R$

- $I_{rms}=\frac{Im}{\sqrt{2}}$

- $V_{rms}=\frac{Vm}{\sqrt{2}}$

- $I(t) = \frac{Vm}{\omega L} \sin (\omega t = \frac{\pi}{2})$

- Current lags by $\pi/2$.

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<footer style = "font-size: 18px">Alternating Current/Voltages $\rightarrow$ Phaser (Resistive cct) $\rightarrow$ <span style = "color:blue"> Pure Inductive Circuit </span> $\rightarrow$ Inductive Reactors $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Capacitive Circuits Alternating Currents L-4 </Success>
### <primary style="font-size:24px"> Example </primary>
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- $V=25 \sin (\omega t)$ in $\omega=400 rad/s$ in 10H inductor.

- At the instant when the voltage is -12.5 V and its magnitude is increasing.

- What is current?

- $V_m=25V$

- $X_L=\omega L=400 \times 10 = 4000 \Omega$

- $I_m=\frac{Vm}{\omega L}=\frac{25}{4000}=6.25 mA$

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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-04-capacitive-circuits-alternating-currents-l-4_10-i67tl_hqxgm-095-0915.6.jpg)

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<footer style = "font-size: 18px">Inductive Reactors $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Example $\rightarrow$ Purely Capacitive Circuit </footer>

### <Success style="font-size:25px"> Capacitive Circuits Alternating Currents L-4 </Success>
### <primary style="font-size:24px"> Example </primary>
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- $V(t)=-12.5 V$

- $\omega t=\frac{7 \pi}{6}$ and $\frac{11 \pi}{6}$

- The magnitude is increasing at $\omega t=\frac{7 \pi}{8}$

- $I(t)=6.25 \sin (\frac{7 \pi}{6}-\frac{\pi}{2})$

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<footer style = "font-size: 18px">Example $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Purely Capacitive Circuit $\rightarrow$ Purely Capacitive Circuit </footer>

### <Success style="font-size:25px"> Capacitive Circuits Alternating Currents L-4 </Success>
### <primary style="font-size:24px"> Phasor Diagram </primary>
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- Current leads the voltage by $\frac{\pi}{2}$.

- I becomes maximum T/4 before its voltage does.

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<footer style = "font-size: 18px">Purely Capacitive Circuit $\rightarrow$ Purely Capacitive Circuit $\rightarrow$ <span style = "color:blue"> Phasor Diagram </span> $\rightarrow$ Phasor Diagram for Capacitive Circuit $\rightarrow$ Phasor Diagram for Capacitive Circuit </footer>

### <Success style="font-size:25px"> Capacitive Circuits Alternating Currents L-4 </Success>
### <primary style="font-size:24px"> Phasor Diagram for Capacitive Circuit </primary>
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- I > 0 charging current, Between T = 0 to t = $\frac{t}{4}$ charging.

- At t = $\frac{T}{4}$ fully charged and there is no current from $\frac{T}{4}$ to $\frac{T}{2}$.

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<footer style = "font-size: 18px">Purely Capacitive Circuit $\rightarrow$ Phasor Diagram $\rightarrow$ <span style = "color:blue"> Phasor Diagram for Capacitive Circuit </span> $\rightarrow$ Phasor Diagram for Capacitive Circuit $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Capacitive Circuits Alternating Currents L-4 </Success>
### <primary style="font-size:24px"> Phasor Diagram for Capacitive Circuit </primary>
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- At t = $\frac{T}{2}$ the fully plates are fully discharged.

- Charging from t = $\frac{T}{2}$ to $\frac{3T}{4}$.

- Current reverses and plates are charged oppositely

- Discharging from $\frac{3T}{4}$ to T.

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<footer style = "font-size: 18px">Phasor Diagram $\rightarrow$ Phasor Diagram for Capacitive Circuit $\rightarrow$ <span style = "color:blue"> Phasor Diagram for Capacitive Circuit </span> $\rightarrow$ Example $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Capacitive Circuits Alternating Currents L-4 </Success>
### <primary style="font-size:24px"> Example </primary>
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- At the instant when V(t) = -12.5 V and is increasing in magnitude

- What is the current?

- $\Chi_C =\frac{1}{\omega C}=\frac{1}{400 \times 10^{-8}}=250\Omega$

- $I_m=\frac{V_m}{X_c}=\frac{25}{250}=0.1A$

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<footer style = "font-size: 18px">Phasor Diagram for Capacitive Circuit $\rightarrow$ Phasor Diagram for Capacitive Circuit $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Example $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Capacitive Circuits Alternating Currents L-4 </Success>
### <primary style="font-size:24px"> Example </primary>
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- Volatage divider using capacitors

- $\Chi_{C_1}=\frac{1}{\omega c_!}=250 \Omega$

- $\Chi_{C_2}=\frac{!}{\omega c_2}=125 \Omega$

- $\Chi_C=250+125=375 \Omega$

- $I_m=\frac{V_m}{X_c}=\frac{25}{375}A=67mA$

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<footer style = "font-size: 18px">Example $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Example $\rightarrow$ Power in a Capacitive Circuit </footer>

### <Success style="font-size:25px"> Capacitive Circuits Alternating Currents L-4 </Success>
### <primary style="font-size:24px"> Example </primary>
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- A $5 \mu F$ is connected to $V_{rms}=60$ V. Observed peak current to be 0.2 A. Find frequency of source.

- $V_{rms}=I_{rms} \Chi_C$

- $\Chi_C=\frac{V_{rms}}{I_{rms}}=\frac{60}{0.3}=200 \Omega$

- $\frac{1}{\omega c}=200 \rightarrow \omega = 1000 rad/s = 2 \pi f$

- $f=\frac{1000}{2 \pi}\simeq 160 Hz.$

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<footer style = "font-size: 18px">Example $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Power in a Capacitive Circuit $\rightarrow$ Power </footer>

### <Success style="font-size:25px"> Capacitive Circuits Alternating Currents L-4 </Success>
### <primary style="font-size:24px"> Power </primary>
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- P(t) = I(t) V(t)$=\frac{I_m V_m}{2}\sin(2 \omega t)$

- (i) First quarter cycle t = 0, t = T/4

- $(\omega t = 0 \neq \pi/2);\sin(2 \omega t) \geq 0$

- I > 0, V > 0, P > 0 : Energy is observed

- (ii) From t = $\frac{T}{4}$ to $\frac{T}{2}$

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<footer style = "font-size: 18px">Example $\rightarrow$ Power in a Capacitive Circuit $\rightarrow$ <span style = "color:blue"> Power </span> $\rightarrow$ Thank You $\rightarrow$  </footer>