physics-class-12-unit-03-chapter-08-equivalent-circuits-l-7-11-vw5crcsfpzs

### <Success style="font-size:25px"> Equivalent Circuits L-7 </Success>
### <primary style="font-size:24px"> Series and Parallel Combination </primary>
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* Series and Parallel Combination

* Parallel Combination

- Voltage across each member is same

- $\Delta V=I_1 R_1=I_2 R_2=I_3 R_3$

* Series Combination

- Same current through each member

- $V_{a b}=I\left(R_1+R_2+R_3\right)$

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<footer style = "font-size: 18px"> $\rightarrow$ Equivalent Circuits $\rightarrow$ <span style = "color:blue"> Series and Parallel Combination </span> $\rightarrow$ Equivalent Circuits $\rightarrow$ Potential Difference </footer>

### <Success style="font-size:25px"> Equivalent Circuits L-7 </Success>
### <primary style="font-size:24px"> Equivalent Circuits </primary>
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- When switch is open

- Ce : $R_1$ is in series with $R_2$

- $ R_{12}=12 \Omega $

- $ R_{34}=20 \Omega$

- $R_{12}$ and $R_{34}$ are parallel

- $\frac{1}{R_{eq}}  =\frac{1}{R_{12}}+\frac{1}{R_{24}}$
- $ =\frac{1}{12}+\frac{1}{20} $

- $R_{eq}  =\frac{15}{2} \Omega$

- $I=\frac{21}{15 / 2}=2.8 \mathrm{~A}$

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<footer style = "font-size: 18px">Equivalent Circuits $\rightarrow$ Series and Parallel Combination $\rightarrow$ <span style = "color:blue"> Equivalent Circuits </span> $\rightarrow$ Potential Difference $\rightarrow$ Potential Difference </footer>

### <Success style="font-size:25px"> Equivalent Circuits L-7 </Success>
### <primary style="font-size:24px"> Potential Difference </primary>
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- $ \Delta V_{c e}=\Delta V_{d f}=21 \mathrm{~V}$

- $ I_1=\frac{21}{12}=1.75 \mathrm{~A} $

- $ I_2=\frac{21}{20}=1.05 \mathrm{~A} $

- $ V_a=21-I_1 R_1=21-\frac{7}{4} \times 4=14 \mathrm{~V}$

- $ V_b=21-I_3 R_3=21-\frac{21}{20} \times 12=8.4 \mathrm{~V}$
	
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<footer style = "font-size: 18px">Series and Parallel Combination $\rightarrow$ Equivalent Circuits $\rightarrow$ <span style = "color:blue"> Potential Difference </span> $\rightarrow$ Potential Difference $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Equivalent Circuits L-7 </Success>
### <primary style="font-size:24px"> Example </primary>
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- $a \equiv a^{\prime} $

- $ b \equiv b^{\prime} $

- $R_1 \|| R_3 \Rightarrow R_{13}  =\frac{R_1 R_3}{R_1+R_3} $

- $ =\frac{48}{16}=3 \Omega $

- $R_2 \|| R_4 \Rightarrow R_{24} =\frac{R_2 R_4}{R_2+R_4} =4 \Omega$

- $I=3 \mathrm{~A}$

- Drop across ca is 9V

- Drop acros ae is  12V

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<footer style = "font-size: 18px">Potential Difference $\rightarrow$ Potential Difference $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Example $\rightarrow$ Net Resistance </footer>

### <Success style="font-size:25px"> Equivalent Circuits L-7 </Success>
### <primary style="font-size:24px"> Example </primary>
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- Drop across $c a=9 v$

- $ I_1=\frac{9}{4}=2.25 \mathrm{~A}$

- Drop across ae = 12

- $ I_2=\frac{12}{7}=1.5 \mathrm{~A} $

- $ I_{a b}=0.75 \mathrm{~A}$

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<footer style = "font-size: 18px">Potential Difference $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Net Resistance $\rightarrow$ Infinite Resistance Network </footer>

### <Success style="font-size:25px"> Equivalent Circuits L-7 </Success>
### <primary style="font-size:24px"> Net Resistance </primary>
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- $R_{\text {eq }}=\frac{2 \times 4}{2+4}=\frac{8}{6}=\frac{4}{3} \Omega$

- Net Resistance

- $R_{\text {final }}=4 \times \frac{4}{3}=\frac{16}{3} \Omega$

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<footer style = "font-size: 18px">Example $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Net Resistance </span> $\rightarrow$ Infinite Resistance Network $\rightarrow$ Infinite Resistance Network </footer>

### <Success style="font-size:25px"> Equivalent Circuits L-7 </Success>
### <primary style="font-size:24px"> Infinite Resistance Network </primary>
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- $R_{eq}$ is Parallel to R

- $ = \frac{R_{e q} \cdot R}{R_{e q}+R}=R_{e q}^{\prime}$

- $ =R_{e q}^{\prime}+2 R=\frac{R_{e q} R}{R_{e q}+R}+2 R $

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<footer style = "font-size: 18px">Example $\rightarrow$ Net Resistance $\rightarrow$ <span style = "color:blue"> Infinite Resistance Network </span> $\rightarrow$ Infinite Resistance Network $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Equivalent Circuits L-7 </Success>
### <primary style="font-size:24px"> Example </primary>
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- $\rho$ Resistivity

- r = a + $ \frac {b-a}{L}$ x

- $d R(x)  =\rho \cdot \frac{d x}{\pi\left[a+\frac{b-a}{L} x\right]^2}$

- $R =\frac{\rho}{\pi} \int_0^L \frac{d x}{\left[a+\frac{b-a}{L} x\right]^2}$

- $ =\frac{\rho}{\pi} \times \frac{b-a}{a b}=\frac{\rho}{\pi} \cdot \frac{L}{a b}$

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<footer style = "font-size: 18px">Infinite Resistance Network $\rightarrow$ Infinite Resistance Network $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Example $\rightarrow$ Series Circuit </footer>

### <Success style="font-size:25px"> Equivalent Circuits L-7 </Success>
### <primary style="font-size:24px"> Example </primary>
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- $ \rho_{A L}^0=2.75 \times 10^{-8} \Omega \mathrm{m}$

- $ \alpha_{A L}=.004 /{ }^{\circ} \mathrm{C}$

- $ \rho_c^0=5 \times 10^{-5} \Omega \mathrm{m}$

- $ \alpha_c=-0.0005 / ^0 \mathrm{C}$

- $R_{A L}+R_C=  R_{A L}^0\left(1+\alpha_{A L} \cdot \Delta T\right) $
- $ +R_c^0\left(1+\alpha_0 \cdot \Delta T\right)$

- $R_{A L}+R_C \equiv R_{A L}^{\circ}+R^{0}_{C}$

- $R_{A L} \alpha_{A L} \cdot \Delta T=-R_{c}^0 \alpha_c \cdot \Delta T$.

- $\alpha_{AL} \rho_{A L}^0 L^{A L}=-\alpha_c \rho_c^{0} \cdot L^C$

- $L^\mu / L^c \approx 227$

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<footer style = "font-size: 18px">Infinite Resistance Network $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Series Circuit $\rightarrow$ Equivalent Circuits </footer>

### <Success style="font-size:25px"> Equivalent Circuits L-7 </Success>
### <primary style="font-size:24px"> Equivalent Circuits </primary>
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- $R_6$ and $R_8$ in series = $ R_{68}$

- $R_9 \|| R_{10}$ $\Rightarrow R_9^{\prime}$

- $R_9 \text{in series with} R_{68}$.
 
 - $R_{689}{'}$ is parallel to $R_7^{\prime}$

- $\Rightarrow R^{\prime}$

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<footer style = "font-size: 18px">Example $\rightarrow$ Series Circuit $\rightarrow$ <span style = "color:blue"> Equivalent Circuits </span> $\rightarrow$ Cells in series $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> Equivalent Circuits L-7 </Success>
### <primary style="font-size:24px"> Cells in series </primary>
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- **More than 1 battery in the circuit**

- **Cells in series**

- $ V_c-I r_2+\varepsilon_2-I r_1+\varepsilon_1=V_a $

- $ V_a-V_c=(\underbrace{\varepsilon_1+\varepsilon_2}_{\varepsilon})-I \underbrace{r_1+r_2})$

- An equivalent emf $\varepsilon_1+\varepsilon_2$ and effective internal resistance

- $r_1+r_2$

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<footer style = "font-size: 18px">Series Circuit $\rightarrow$ Equivalent Circuits $\rightarrow$ <span style = "color:blue"> Cells in series </span> $\rightarrow$ Thank You $\rightarrow$  </footer>