physics-class-12-unit-03-chapter-10-series-parallel-combinations-of-cell-currentelectricity-l-8-11-df3eda3gabu

### <Success style="font-size:25px"> Series Parallel Combinations Of Cell Currentelectricity L-8 </Success>
### <primary style="font-size:24px"> Cells Combination </primary>
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- **Series:**

- I remains the same $\Delta V$ different

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

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

- $ \varepsilon_{e q}=\varepsilon_1+\varepsilon_2 $

- $ r_{eq}=r_1+r_2 $

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<footer style = "font-size: 18px"> $\rightarrow$ Series and Parallel Combinations of Cells $\rightarrow$ <span style = "color:blue"> Cells Combination </span> $\rightarrow$ Cells Series $\rightarrow$ Cells in Parallel </footer>

### <Success style="font-size:25px"> Series Parallel Combinations Of Cell Currentelectricity L-8 </Success>
### <primary style="font-size:24px"> Cells Series </primary>
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- $V_c-I r_2-\varepsilon_2-I r_1+\varepsilon_1  =V_a $

- $ V_a-V_c=\left(\varepsilon_1-\varepsilon_2\right)-I\left(r_1+r_2\right)$

- Capacity Rating of a battery

- Lead Acid: $2 \mathrm{~V}$

- $ A A - 1.5 V $

- $ A A A - 1.5 V $

- $ N i - cd = -1.2 V $

- $ L i- ion - 3.6 V$

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<footer style = "font-size: 18px">Series and Parallel Combinations of Cells $\rightarrow$ Cells Combination $\rightarrow$ <span style = "color:blue"> Cells Series </span> $\rightarrow$ Cells in Parallel $\rightarrow$ Equivalent Resistance </footer>

### <Success style="font-size:25px"> Series Parallel Combinations Of Cell Currentelectricity L-8 </Success>
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- $ V=V_{B1}-V_{B2} \Rightarrow \varepsilon_1-I_1 r_1=\varepsilon_2-I_2 r_1 $

- $ I=I_1+I_2 $

- $ =\frac{\varepsilon_1-v}{r_1}+\frac{\varepsilon_2-v}{r_1} $

- $ =\left(\frac{\varepsilon_1}{r_1}+\frac{\varepsilon_2}{r_2}\right)-v\left(\frac{1}{r_1}+\frac{1}{r_2}\right)$

- V= -I $\frac{r_1.r_2}{r_1+r_2}$ + $\frac{\varepsilon_1 r_2+\varepsilon_2 r_1}{r_1 + r_2}$

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<footer style = "font-size: 18px">Cells Combination $\rightarrow$ Cells Series $\rightarrow$ <span style = "color:blue"> Cells in Parallel </span> $\rightarrow$ Equivalent Resistance $\rightarrow$ Example-1 </footer>

### <Success style="font-size:25px"> Series Parallel Combinations Of Cell Currentelectricity L-8 </Success>
### <primary style="font-size:24px"> Equivalent Resistance </primary>
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- $ r_{eq} = \Delta \frac{r_1 r_2}{r_1+r_2} \text { Equivalent } $

- $ \text { resistance for }$ $ r_1 || r_2 $

- $ \varepsilon_{eq}=\frac{\varepsilon_1 r_2+\varepsilon_2 r_1}{r_1+r_2} $

- $ =\left[\frac{\varepsilon_1 r_2+\varepsilon_2 r_1}{r_1 r_2}\right] \times \frac{r_1 r_2}{r_1+r_2}$

- $ =\left(\frac{\varepsilon_1}{r_1}+\frac{\varepsilon_1}{r_2}\right) \times r_{eq}$

- $ \frac{\varepsilon_{eq}}{r_{eq}}=\frac{\varepsilon_1}{r_1}+\frac{\varepsilon_2}{r_2}$

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<footer style = "font-size: 18px">Cells Series $\rightarrow$ Cells in Parallel $\rightarrow$ <span style = "color:blue"> Equivalent Resistance </span> $\rightarrow$ Example-1 $\rightarrow$ Example-1 </footer>

### <Success style="font-size:25px"> Series Parallel Combinations Of Cell Currentelectricity L-8 </Success>
### <primary style="font-size:24px"> Example-1 </primary>
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- No Current

- $ r_{eq} = \frac {1}{3}\Omega$

- $\frac{\varepsilon_{eq}}{r_{eq}}=\frac{\varepsilon_1}{r_1}+\frac{\varepsilon_2}{r_2}+\frac{\varepsilon_3}{r_3}=6 $

- $\varepsilon_{eq}=6 \times \frac{1}{3}=2 V$

- $3-1 \times I_1=2 $

- $I_1=1 \mathrm{~A} $

- $2-1 \times I_2=2 \Rightarrow I_2=0 $

- $I_3=-1 \mathrm{~A}$

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<footer style = "font-size: 18px">Cells in Parallel $\rightarrow$ Equivalent Resistance $\rightarrow$ <span style = "color:blue"> Example-1 </span> $\rightarrow$ Example-1 $\rightarrow$ Example-1 </footer>

### <Success style="font-size:25px"> Series Parallel Combinations Of Cell Currentelectricity L-8 </Success>
### <primary style="font-size:24px"> Example-1 </primary>
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- $I=I_1+I_2+I_3$

- $ \varepsilon_1-I_1 \times 1-\left(I_1+I_2+I_3\right) \times 1=0 $

- $ 3=2 I_1+I_2+I_3 \quad(1)$

- $ I_1=\varepsilon_1-\varepsilon_2=1 \Rightarrow I_1=1 \mathrm{~A}$

- $ I_3=-1 \mathrm{~A}$

- $ I_2=2 \mathrm{~A}$

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<footer style = "font-size: 18px">Equivalent Resistance $\rightarrow$ Example-1 $\rightarrow$ <span style = "color:blue"> Example-1 </span> $\rightarrow$ Example-1 $\rightarrow$ Example-1 </footer>

### <Success style="font-size:25px"> Series Parallel Combinations Of Cell Currentelectricity L-8 </Success>
### <primary style="font-size:24px"> Example-1 </primary>
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- $ I_1=I_2 $

- $ r_{eq}=.075 \Omega $

- $\frac{\varepsilon_{eq}} {.075}$ = $\frac{2 \times 1.2}{0.15}$

- $\varepsilon_{e q}=1.2 \mathrm{~V} $

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<footer style = "font-size: 18px">Example-1 $\rightarrow$ Example-1 $\rightarrow$ <span style = "color:blue"> Example-1 </span> $\rightarrow$ Example-1 $\rightarrow$ Kirchhoff's Law </footer>

### <Success style="font-size:25px"> Series Parallel Combinations Of Cell Currentelectricity L-8 </Success>
### <primary style="font-size:24px"> Kirchhoff's Law </primary>
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- **Junction**

- A point in the circuit, Where three or more conductors are joined together.

- **Loops**

- Any closed path in the circuit.

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<footer style = "font-size: 18px">Example-1 $\rightarrow$ Example-1 $\rightarrow$ <span style = "color:blue"> Kirchhoff's Law </span> $\rightarrow$ Example $\rightarrow$ Kirchhoff's Laws </footer>

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### <primary style="font-size:24px"> Kirchhoff's Laws </primary>
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* Junction Rule

- Algebraic sum of currents arriving at a junction is zero.

- $\sum_i I_i=0$

- if $I_1, I_2, \ldots I_5$ are just magnitudes.

- $I_1+I_3+I_4-I_2-I_5=0$

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<footer style = "font-size: 18px">Kirchhoff's Law $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Kirchhoff's Laws </span> $\rightarrow$ Loop Rule $\rightarrow$ EMF </footer>

### <Success style="font-size:25px"> Series Parallel Combinations Of Cell Currentelectricity L-8 </Success>
### <primary style="font-size:24px"> EMF </primary>
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- In the seat of emf

- $\Delta v>0$ if we are going from the negative terminal to positive terminal.

- $\Delta v<0$ if we are going from positive to negative.

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<footer style = "font-size: 18px">Kirchhoff's Laws $\rightarrow$ Loop Rule $\rightarrow$ <span style = "color:blue"> EMF </span> $\rightarrow$ Example $\rightarrow$ Thank You </footer>