Two identical cells of emf 7 V and internal resistance 1 Ω are connected in series across a 5 Ω resistance. The current in the resistance will be:

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.
• For a cell of emf E and internal resistance r,

⇒ E - V = Ir

Where I = current, and V = potential difference across external resistance

Cells in series:

• If the number of cells is connected end to end then it is called a series arrangement of cells.
• The equivalent emf of cells in series arrangement is given as,

⇒ E_eq = E₁ + E2 +...+ En

• The equivalent internal resistance of cells in a series arrangement is given as,

⇒ req = r1 + r2 +...+ rn

CALCULATION:

Given:

E₁ = E₂ = 7V, r₁ = r₂ = 1Ω, and R = 5Ω

• The two cells are connected in series so the equivalent emf is given as,

⇒ Eeq = E1 + E2

⇒ Eeq = 7 + 7

⇒ Eeq = 14 V     -----(1)

• And the equivalent resistance is given as,

⇒ req = r1 + r2

⇒ req = 1 + 1

⇒ req = 2 Ω

• The equivalent resistance of the circuit is given as,

⇒ R_eq = R + req

⇒ Req = 5 + 2

⇒ Req = 7 Ω     -----(2)

By Ohm's law,

\(⇒ I=\frac{V}{R_{eq}}\)

\(⇒ I=\frac{14}{7}\)

⇒ I = 2 A

• Hence, option 1 is correct.