What will be the current flowing in a circuit containing n identical cells of EMF 'E' and internal resistance 'r' each connected in series and external resistance R.

CONCEPT:

• EMF of a cell: Maximum potential difference between two electrodes when no current is drawn from the cell is called electromotive force or EMF of a cell.
  • SI unit of EMF is V or JC-1
• Internal resistance of a cell: When electric current flows through the cell, the value of resistance offered by the electrodes and electrolyte is called the internal resistance of a cell.

• In a closed circuit, the potential difference between the electrodes is called the terminal potential difference.
• The terminal potential difference can be calculated as

⇒ V = E - IR​

Where E = EMF of the cell, I is current and r is the internal resistance. 

• When the key is closed, current flows through the circuit, there is a drop in potential across internal resistance and external resistance R.
• The total resistance of the circuit R + r, where r is the internal resistance and R is the external resistance.
• The electric current in the circuit can be calculated as  

\(⇒ i=\frac{E }{R+r}\)

EXPLAINATION:

As we know, when 'n' cells are connected in series, then the net e.m.f (E') = nE and net internal resistance (r') = nr

As we know, according to the ohms law, the potential difference across R is

⇒ V = IR​

\(\Rightarrow I=\frac{E' }{r'+R}\),

\(⇒ I=\frac{nE }{nr+R}\)

• Hence the correct option is 4)

Additional Information

Electrolyte cell:

• A simple device to maintain a steady current in the electric cell is called an electrolytic cell

• An electrolytic cell consists of a negative electrode, a positive electrode, and an electrolyte.
  • Exchange of charges takes place when electrodes are immersed in the electrolyte. 
  • The positive electrode (anode) acquires positive potential and the negative electrode (cathode) acquires negative potential