Question

Under what condition, the current passing through the resistance $R$ can be increased by short-circuiting the battery of emf $E_{2}$. The internal resistances of the two batteries are $r_{1}$ and $r_{2}$, respectively.

• A. $E_{2} r_{1} > E_{1}\left(R+r_{2}\right)$
• B. $E_{1} r_{2} > E_{2}\left(R+r_{1}\right)$
• C. $E_{2} r_{2} > E_{1}\left(R+r_{2}\right)$
• D. $E_{1} r_{1} > E_{2}\left(R+r_{1}\right)$

Answer 1

Answer: (B)

Current through $R$ before short-circuiting second cell
$I=\frac{E_{1}+E_{2}}{R+\left(r_{1}+r_{2}\right)}$
Current through $R$ after short-circuiting second cell
$I'=\frac{E_{1}}{R+r_{1}}$
Here, $I' > I$ or $E_{1} r_{2} > E_{2}\left(R+r_{1}\right)$