Parallel Combination of Cells

A cell is an important device in an electrical circuit, it is used to transfer electrical energy to the circuit. The cells are connected to two terminals: Anode and Cathode. The anode is the positive terminal, and the cathode is the negative terminal. The current flows out of the anode and enters the cathode. The difference in charge of the two terminals of the cell will create a potential difference across the circuit. The potential difference produced is called the electromotive force or EMF of the cell. This EMF causes the flow of electric current in the circuit.

More than one cell connected together is called the battery. The cells are connected either in series or parallel. In a series combination, there is only a single path between the terminals of the cell. The positive terminal of the cell is connected to the negative terminal of the other cell in a series combination. Parallel combination circuits have multiple paths between the terminals. In a parallel combination of cells, all the positive terminals of the cells are connected together, and the negative terminals of the cells are connected together.

Parallel Combination of Cells

When the cells are connected in parallel, the current will be divided among various cells. From the figure, we can see that two cells are connected in parallel. The emf of cell 1 is ε_1, and the emf of cell 2 is ε₂. The internal resistance of cell 1 is r_1, and cell 2 is r₂. The current is split into i₁ and i₂. The total current i = i₁ + i₂

The resultant internal resistance of the combination is,

The equivalent EMF ( ε_eq) is equal to the potential difference between A and B (V_A – V_B) when it is not in use. To determine the equivalent EMF, we should apply Kirchoff’s loop rule.

From the figure above, we get

– ε₁ + ir₁ + ir₂ + ε₂ = 0

⇒ i = ε₁– ε₂/(r₁ + r₂) ——(1)

The potential difference V_A – V_B = ε₁– ir₁

Or V_A – V_B = ε₂+ ir₂

Substituting the value of ‘i’ in either of the two equations above, we get

V_A – V_B = ε₂+ ir₂

= (ε₂r₁+ ε₁r₂)/(r₁ + r₂)

Considering the equation of resultant internal resistance, the above expression can be written as

Advantages of Cells Connected in Parallel

(1) If any one of the cells connected in parallel is damaged, the other cells are not affected.

(2) If the cells are connected in parallel, they will not exhaust easily.

Disadvantages of Cells Connected in Parallel

(1) The voltage developed will not be increased by increasing the number of cells in the parallel combination.

(2) The output power is based on one cell. Therefore, the brightness of the bulb connected will not be very high.

Solved Examples

(1) From the given circuit

Find

(i) Equivalent EMF

(ii) Equivalent internal resistance

(iii) Total current

(iv) Potential difference across each cell

(v) Current from each cell

Solution:

(i) There are four paths through the circuit. The potential difference across each path is 5 V. This will be equal to the EMF of each cell. This means that the total EMF provided by the combination is also 5 Volts.

(ii) Since there are 4 cells with internal resistance 0.5Ω connected in parallel, the equivalent internal resistance is given by the formula

r_eq = 0.5/4 = 0.125 Ω

(or)

r_eq = r/n = 0.5/4 = 0.125 Ω

(iii) Total current, I = ε/ (R + r/n)

I = 5 / (10 + 0.125)

= 5/ 10.125

= 0.5 A

(iv) Potential difference V = IR = 0.5 x 10 = 5 V

(v) Current from each cell

I’ = I/n

= 0.5/4 = 0.125 A

(2) If two cells with equivalent internal resistances 2 ohms are connected in parallel, what would be the value of the resistance of each cell if both have the same value?

Solution:

Given

r₁ = r₂

½ = 2/r₁

r₁ = 4 Ω = r₂

Recommended Videos

Parallel Combination of Cells

Series, Parallel and Mixed Combination of Cells