If the series arrangement of two similar cells of emf E and internal resistance r is connected to a load of resistance R, then find the current in the load resistance.

CONCEPT:

Cell

• The cell converts chemical energy into electrical energy.
• Cells are of two types:
  1. Primary cell: This type of cell cannot be recharged.
  2. Secondary cell: This type of cell can be recharged.

The electromotive force of a cell

• It is the maximum potential difference between the two electrodes of the cell when the cell is in an open circuit.

The potential difference of a cell

• It is the maximum potential difference between the two electrodes of the cell when the cell is in a closed circuit.

If a cell of emf E and internal resistance r is connected across a load resistance R, then the current in the load resistance is given as,

\(⇒ I=\frac{E}{R+r}\)

Cells in series:

• A set of batteries are said to be connected in series when the positive terminal of one cell is connected to the negative terminal of the succeeding cell.
• The equivalent emf of the series arrangement is given as,

​⇒ E_eq = E₁ + E₂ + ... + E_n

The equivalent internal of the series arrangement is given as,

​⇒ req = r1 + r2 + ... + rn

CALCULATION:

Given E₁ = E₂ = E, r1 = r2 = r, Load resistance R = R

The equivalent emf of the series arrangement is given as,

⇒ Eeq = E1 + E2

⇒ Eeq = E + E

⇒ Eeq = 2E      ----(1)

The equivalent internal resistance of the series arrangement is given as,

⇒ req = r1 + r2

⇒ req = r + r

⇒ req = 2r      ----(2)

We know that if a cell of emf E and internal resistance r is connected across a load resistance R, then the current in the load resistance is given as,

\(⇒ I=\frac{E}{R+r}\)      ----(3)

By equation 1, equation 2, and equation 3 if the series arrangement of two similar cells of emf E and internal resistance r is connected to a load of resistance R, then the current in the load resistance is given as,

\(⇒ I=\frac{E_{eq}}{R+r_{eq}}\)

\(⇒ I=\frac{2E}{R+2r}\)

Hence, option 3 is correct.