Question

In order to determine the e.m.f. of a storage battery it was connected in series with a standard cell (both are adding) in a certain circuit and a current $I_{1}$ was obtained. When polarity of the standard cell is reversed, a current $I_{2}$ was obtained in the same direction as that of $I_{1}$. What is the e.m.f. $\varepsilon_{1}$ of the storage battery? The e.m.f. of the standard cell is $\varepsilon_{2}$.

• A. $\varepsilon_{1}=\frac{I_{1}+I_{2}}{I_{1}-I_{2}} \varepsilon_{2}$
• B. $\varepsilon_{1}=\frac{I_{1}+I_{2}}{I_{2}-I_{1}} \varepsilon_{2}$
• C. $\varepsilon_{1}=\frac{I_{1}-I_{2}}{I_{1}+I_{2}} \varepsilon_{2}$
• D. $\varepsilon_{1}=\frac{I_{2}-I_{1}}{I_{1}+I_{2}} \varepsilon_{2}$

Answer 1

Answer: (A)

$\varepsilon_{1}+\varepsilon_{2}=I_{1} R, \varepsilon_{1}-\varepsilon_{2}=I_{2} R$
Dividing above two equations, $\varepsilon_{1}=\left(\frac{I_{1}+I_{2}}{I_{1}-I_{2}}\right) \varepsilon_{2}$