Relationship between EMF of a cell (E) , terminal voltage (V) and internal resistance (r).

# Relationship between EMF of a cell (E) , terminal voltage (V) and internal resistance (r).

In above figure shows the general Electric circuit containing external resistance R ohm when E volt electromotive force is applied in the circuit then current I flowing through the external resistance and the potential difference V volt is produced across its ends.

Current drawn from       ( EMF of cell )
a cell in the circuit.     =         ÷
                                            Total resistance

            I = E / (R+r)
  RI + Ir = E

( By ohm's law , V = RI )

V + Ir = E

Or , [V = E - Ir]--------(1)
This is terminal voltage at discharging process

And. [ V = E + Ir ]
This is terminal voltage at charging process


Again by ohm's law : I = V/R

This value of I is putting in enq(1)

V = E - ( V/R )r

(V/R)r = E - V

Vr = R ( E - V )

r = R ( E - V )/V

r = R ( E/V - V/V )

{ r = R ( E/V - 1) }