question_answer

The potential difference across the terminals of a battery is 50 V when 11A current is drawn and 60 V when 1 A current is drawn. The emf and the internal resistance of the battery are

A)  \[62\text{ }V,\text{ }2\,\Omega \]         

B)  \[63\text{ }V,\text{1}\,\Omega \]

C)  \[61\text{ }V,\text{ 1}\,\Omega \]        

D)  \[64\text{ }V,2\,\Omega \]

Correct Answer: C

Solution :

                 For a closed circuit, cell supplies a constant current in the circuit. Equation of cell \[E=V+Ir\] For V = 50 volt \[E=50+11r\]                      ...(i) Similarly for V = 60 volt \[E=60+r\]                            ...(ii) From Eqs. (i) and (ii), we get \[r=1\,\Omega \] Substituting the value of r in Eq (i), we get \[E=61\,V\]