Test: Combination of Cells - JEE MCQ

Components connected in parallel provide alternative pathways for current flow. When cells are connected in parallel, the total voltages that they provide does not change. For example, when two or more 2 V cells are connected in parallel, they still provide a total voltage of 2 V.

In series connection of cells total internal resistance=nr total resistance of circuit=nR current is same potential difference is different so,I=nv/nR+nr I=V/R+r current is same as before in parallel connection of cells total internal resistance=r/n total resistance of circuit=R/n total current=nI potential difference is same nI=V/r/n+R/n I=V/R+r current is same as before.

Total emf = 3 x 4 = 12 V
Total resistance = 6 + 3r
Current in the circuit = 2 A
Using ohm's law
2 = 12/ (6+3r)
2(6+3r)=12
12+6r=12
6r = 12-12 = 0
r = 0/6 = 0

The voltage developed by the cells in parallel connection cannot be increased by increasing the number of cells present in the circuit. It is because they do not have the same circular path. In parallel connection the connection provides power based on one cell.
The voltage will remain the same.

When resistors are connected in series, the current through each resistor
remains the same.
The total voltage across all the resistors is equal to the sum of the
voltages across each resistor.

When we connect cells to form a battery, we join opposite ends(+ve with -ve and vice versa) to get supporting emf, i.e. net emf get added, but when we join the same polarities(-ve with -ve, like in the question), they oppose each other, hence net emf is the difference b/w them.
The expression for equivalent emf when two cells of emf’s
ε_eq = ε₁ - ε₂ (ε₁> ε₂)

1^st case[series]
I=E+E/r+r+1-----1
2^nd case[parallel]
I=E[E will be same in parallel]/(1/r)+(1/r)+(1/1)----2
Current in both cases are the same.
1=2
2E/2r+1=E/(2/r)+1
R=1 Ω

In series, cells are joined end to end so that the same current flows through each cell.  In case if the cells are connected in series the emf of the battery is connected to the sum of the emf of the individual cells. Suppose we have multiple cells and they are arranged in such a way that the positive terminal of one cell is connected to the negative terminal of the other and then again the negative terminal is connected to the positive terminal and so on, then we can that the cell is connected in series.

From the Question,

• Emf (E) = 2 V

• Internal Resistance (r) = 0.2 Ω

• Resistance (R) = 7.4 Ω

Three cells of 2V and 0.2 each are connected in series.

Consider two cells connected to each other.

The total potential difference would be :

Total Potential Difference in a cell is given as :

V=E-IR

Thus,

⇒E-Ir=E1-Ir₁+E₂+Ir₂

⇒E_eq=E₁+E₂ and r_eq=r₁+r₂

Therefore,

For three cells each of emf 2V,

E=2+2+2=6V

For three cells with internal resistance 0.2 Ω,

R=.02+.02+.02=0.6 Ω

We know that,

I=E/r+R

Implies,

 I=6/0.6+7.4

I=6/8

 I=0.75A