Series Parallel Combinations Of Cell Currentelectricity L-8 Series and Parallel Combinations of Cells
→ \rightarrow → → \rightarrow → Series and Parallel Combinations of Cells → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Cells Combination
Series:
I remains the same Δ V \Delta V Δ V
V c − I r 2 + ε 2 − I r 1 + ε 1 = V a V_c-I r_2+\varepsilon_2-I r_1+\varepsilon_1=V_a V c − I r 2 + ε 2 − I r 1 + ε 1 = V a
V a − V c V_a-V_c V a − V c ( ε 1 + ε 2 ) − I ( r 1 + r 2 ) ({\varepsilon_1 + \varepsilon_2})-I({r_1+r_2}) ( ε 1 + ε 2 ) − I ( r 1 + r 2 )
ε e q = ε 1 + ε 2 \varepsilon_{e q}=\varepsilon_1+\varepsilon_2 ε e q = ε 1 + ε 2
r e q = r 1 + r 2 r_{eq}=r_1+r_2 r e q = r 1 + r 2
→ \rightarrow → → \rightarrow → Cells Combination → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Cells Series
V c − I r 2 − ε 2 − I r 1 + ε 1 = V a V_c-I r_2-\varepsilon_2-I r_1+\varepsilon_1 =V_a V c − I r 2 − ε 2 − I r 1 + ε 1 = V a
V a − V c = ( ε 1 − ε 2 ) − I ( r 1 + r 2 ) V_a-V_c=\left(\varepsilon_1-\varepsilon_2\right)-I\left(r_1+r_2\right) V a − V c = ( ε 1 − ε 2 ) − I ( r 1 + r 2 )
Capacity Rating of a battery
Lead Acid: 2 V 2 \mathrm{~V} 2 V
A A − 1.5 V A A - 1.5 V AA − 1.5 V
A A A − 1.5 V A A A - 1.5 V AAA − 1.5 V
N i − c d = − 1.2 V N i - cd = -1.2 V N i − c d = − 1.2 V
L i − i o n − 3.6 V L i- ion - 3.6 V L i − i o n − 3.6 V
Series and Parallel Combinations of Cells → \rightarrow → → \rightarrow → Cells Series → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Cells in Parallel
V = V B 1 − V B 2 ⇒ ε 1 − I 1 r 1 = ε 2 − I 2 r 1 V=V_{B1}-V_{B2} \Rightarrow \varepsilon_1-I_1 r_1=\varepsilon_2-I_2 r_1 V = V B 1 − V B 2 ⇒ ε 1 − I 1 r 1 = ε 2 − I 2 r 1
I = I 1 + I 2 I=I_1+I_2 I = I 1 + I 2
= ε 1 − v r 1 + ε 2 − v r 1 =\frac{\varepsilon_1-v}{r_1}+\frac{\varepsilon_2-v}{r_1} = r 1 ε 1 − v + r 1 ε 2 − v
= ( ε 1 r 1 + ε 2 r 2 ) − v ( 1 r 1 + 1 r 2 ) =\left(\frac{\varepsilon_1}{r_1}+\frac{\varepsilon_2}{r_2}\right)-v\left(\frac{1}{r_1}+\frac{1}{r_2}\right) = ( r 1 ε 1 + r 2 ε 2 ) − v ( r 1 1 + r 2 1 )
V= -I r 1 . r 2 r 1 + r 2 \frac{r_1.r_2}{r_1+r_2} r 1 + r 2 r 1 . r 2 ε 1 r 2 + ε 2 r 1 r 1 + r 2 \frac{\varepsilon_1 r_2+\varepsilon_2 r_1}{r_1 + r_2} r 1 + r 2 ε 1 r 2 + ε 2 r 1
Cells Combination → \rightarrow → → \rightarrow → Cells in Parallel → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Equivalent Resistance
r e q = Δ r 1 r 2 r 1 + r 2 Equivalent r_{eq} = \Delta \frac{r_1 r_2}{r_1+r_2} \text { Equivalent } r e q = Δ r 1 + r 2 r 1 r 2 Equivalent
resistance for \text { resistance for } resistance for r 1 ∣ ∣ r 2 r_1 || r_2 r 1 ∣∣ r 2
ε e q = ε 1 r 2 + ε 2 r 1 r 1 + r 2 \varepsilon_{eq}=\frac{\varepsilon_1 r_2+\varepsilon_2 r_1}{r_1+r_2} ε e q = r 1 + r 2 ε 1 r 2 + ε 2 r 1
= [ ε 1 r 2 + ε 2 r 1 r 1 r 2 ] × r 1 r 2 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} = [ r 1 r 2 ε 1 r 2 + ε 2 r 1 ] × r 1 + r 2 r 1 r 2
= ( ε 1 r 1 + ε 1 r 2 ) × r e q =\left(\frac{\varepsilon_1}{r_1}+\frac{\varepsilon_1}{r_2}\right) \times r_{eq} = ( r 1 ε 1 + r 2 ε 1 ) × r e q
ε e q r e q = ε 1 r 1 + ε 2 r 2 \frac{\varepsilon_{eq}}{r_{eq}}=\frac{\varepsilon_1}{r_1}+\frac{\varepsilon_2}{r_2} r e q ε e q = r 1 ε 1 + r 2 ε 2
Cells Series → \rightarrow → → \rightarrow → Equivalent Resistance → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Example-1
No Current
r e q = 1 3 Ω r_{eq} = \frac {1}{3}\Omega r e q = 3 1 Ω
ε e q r e q = ε 1 r 1 + ε 2 r 2 + ε 3 r 3 = 6 \frac{\varepsilon_{eq}}{r_{eq}}=\frac{\varepsilon_1}{r_1}+\frac{\varepsilon_2}{r_2}+\frac{\varepsilon_3}{r_3}=6 r e q ε e q = r 1 ε 1 + r 2 ε 2 + r 3 ε 3 = 6
ε e q = 6 × 1 3 = 2 V \varepsilon_{eq}=6 \times \frac{1}{3}=2 V ε e q = 6 × 3 1 = 2 V
3 − 1 × I 1 = 2 3-1 \times I_1=2 3 − 1 × I 1 = 2
I 1 = 1 A I_1=1 \mathrm{~A} I 1 = 1 A
2 − 1 × I 2 = 2 ⇒ I 2 = 0 2-1 \times I_2=2 \Rightarrow I_2=0 2 − 1 × I 2 = 2 ⇒ I 2 = 0
I 3 = − 1 A I_3=-1 \mathrm{~A} I 3 = − 1 A
Cells in Parallel → \rightarrow → → \rightarrow → Example-1 → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Example-1
I = I 1 + I 2 + I 3 I=I_1+I_2+I_3 I = I 1 + I 2 + I 3
ε 1 − I 1 × 1 − ( I 1 + I 2 + I 3 ) × 1 = 0 \varepsilon_1-I_1 \times 1-\left(I_1+I_2+I_3\right) \times 1=0 ε 1 − I 1 × 1 − ( I 1 + I 2 + I 3 ) × 1 = 0
3 = 2 I 1 + I 2 + I 3 ( 1 ) 3=2 I_1+I_2+I_3 \quad(1) 3 = 2 I 1 + I 2 + I 3 ( 1 )
I 1 = ε 1 − ε 2 = 1 ⇒ I 1 = 1 A I_1=\varepsilon_1-\varepsilon_2=1 \Rightarrow I_1=1 \mathrm{~A} I 1 = ε 1 − ε 2 = 1 ⇒ I 1 = 1 A
I 3 = − 1 A I_3=-1 \mathrm{~A} I 3 = − 1 A
I 2 = 2 A I_2=2 \mathrm{~A} I 2 = 2 A
Equivalent Resistance → \rightarrow → → \rightarrow → Example-1 → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Example-1
I 1 = I 2 I_1=I_2 I 1 = I 2
r e q = .075 Ω r_{eq}=.075 \Omega r e q = .075Ω
ε e q .075 \frac{\varepsilon_{eq}} {.075} .075 ε e q 2 × 1.2 0.15 \frac{2 \times 1.2}{0.15} 0.15 2 × 1.2
ε e q = 1.2 V \varepsilon_{e q}=1.2 \mathrm{~V} ε e q = 1.2 V
Example-1 → \rightarrow → → \rightarrow → Example-1 → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Example-1
− 2 I 1 × 2 − I 1 × 0.15 + 1.2 = 0 -2 I_1 \times 2-I_1 \times 0.15+1.2=0 − 2 I 1 × 2 − I 1 × 0.15 + 1.2 = 0
I 1 ( 4 + 0.15 ) = 1.2 I_1(4+0.15)=1.2 I 1 ( 4 + 0.15 ) = 1.2
I 1 = 1.2 4 + 0.15 A I_1=\frac{1.2}{4+0.15} A I 1 = 4 + 0.15 1.2 A
Actual Current
2 I 1 = 2.4 4 + 0.15 2 I_1=\frac{2.4}{4+0.15} 2 I 1 = 4 + 0.15 2.4
=1.2 2 + 0.075 \frac{1.2}{2+0.075} 2 + 0.075 1.2
Example-1 → \rightarrow → → \rightarrow → Example-1 → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Kirchhoff's Law
Junction
A point in the circuit, Where three or more conductors are joined together.
Loops
Any closed path in the circuit.
Example-1 → \rightarrow → → \rightarrow → Kirchhoff's Law → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Example
Example-1 → \rightarrow → → \rightarrow → Example → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Kirchhoff's Laws
Junction Rule
Algebraic sum of currents arriving at a junction is zero.
∑ i I i = 0 \sum_i I_i=0 ∑ i I i = 0
if I 1 , I 2 , … I 5 I_1, I_2, \ldots I_5 I 1 , I 2 , … I 5
I 1 + I 3 + I 4 − I 2 − I 5 = 0 I_1+I_3+I_4-I_2-I_5=0 I 1 + I 3 + I 4 − I 2 − I 5 = 0
Kirchhoff's Law → \rightarrow → → \rightarrow → Kirchhoff's Laws → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Loop Rule
Example → \rightarrow → → \rightarrow → Loop Rule → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 EMF
Kirchhoff's Laws → \rightarrow → → \rightarrow → EMF → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Example
I , I 1 , I 2 , I 3 , I 4 , I 5 I, I_1, I_2, I_3, I_4, I_5 I , I 1 , I 2 , I 3 , I 4 , I 5
Loop Rule → \rightarrow → → \rightarrow → Example → \rightarrow → → \rightarrow →
Series Parallel Combinations Of Cell Currentelectricity L-8 Thank You
EMF → \rightarrow → → \rightarrow → Thank You → \rightarrow → → \rightarrow →
Resume presentation
Series Parallel Combinations Of Cell Currentelectricity L-8 Series and Parallel Combinations of Cells $\rightarrow$ $\rightarrow$ Series and Parallel Combinations of Cells $\rightarrow$ Cells Combination $\rightarrow$ Cells Series
