6 Cell, Emf, Internal Resistance Cells in Series and Parallel

Cell, Emf, Internal Resistance Cells in Series and Parallel

Emf

Potential difference between the two poles of the cell in an open circuit is called emf of the cell.

SI unit is volt (V).

Internal resistance (r) of cell

Resistance offered by the electrolyte of the cell when the electric current flows through it

E − emf of cell

r − Internal resistance of the cell

R − External resistance

K − Key

V − Voltmeter

The key K is closed and a current I flows in the circuit.

According to Ohm’s law,

Let V be the terminal potential difference. The terminal potential difference V is less than emf E of the cell by an equal amount, which is equal to potential drop across external resistance R i.e.,

∴ V = E − Ir

Also, terminal potential difference is equal to potential differences across external resistance.

V = IR

From equation (1),

Combination of cells

Cells in Series

E₁ E₂ − emf of two cells

r₁, r₂ − Internal resistance of two cells

I − Current in the circuit

Terminal potential difference across the first cell, V₁ = E₁ − Ir₁

Terminal potential difference across the second cell, V₂ = E₂ − Ir₂

Potential difference between the points A and B,

V = V₁ + V₂ = (E₁ − Ir₁) + (E₂ − Ir₂)

= (E₁ + E₂) − I (r₁ + r₂)

Let

E − Effective emf

r − Effective internal resistance

V = E − Ir

∴ E = E₁ + E₂

r = r₁ + r₂

Current in the circuit,

If the two cells are connected in opposite direction, then

E = E₁ − E₂

Cell in Parallel

E₁, E₂ − emf of two cells

r₁, r₂ − Internal resistances of cell

I₁, I₂ − Current due to the two cells

Terminal potential difference across the first cell,

V = E₁ − I₁r₁

For the second cell,

Let E be effective emf and r is effective internal resistance.

V = E − Ir

And,

Mixed Grouping of Cells

Suppose ‘n’ cells of emf ‘E’ and internal resistance ‘r’ are connected in series in each branch; and there are ‘m’ such branches. ‘R’ is the external resistance connected to the circuit.