Under what condition, the current passing through the resistance R can be increased by short-circuiting the battery of emf E2. The internal resistances of the two batteries are r1 and r2, respectively.

Question

Under what condition, the current passing through the resistance R can be increased by short-circuiting the battery of emf E2. The internal resistances of the two batteries are r1 and r2, respectively. (A) E2 r1 > E1(R+r2) (B) E1 r2 > E2(R+r1) (C) E2 r2 > E1(R+r2) (D) E1 r1 > E2(R+r1)

Tardigrade Admin · Accepted Answer

Current through R before short-circuiting second cell I=(E1+E2/R+(r1+r2)) Current through R after short-circuiting second cell I'=(E1/R+r1) Here, I' > I or E1 r2 > E2(R+r1)

Q. 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.

$E_{2} r_{1} > E_{1} (R + r_{2})$

$E_{1} r_{2} > E_{2} (R + r_{1})$

$E_{2} r_{2} > E_{1} (R + r_{2})$

$E_{1} r_{1} > E_{2} (R + r_{1})$

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

Q. Under what condition, the current passing through the resistance R can be increased by short-circuiting the battery of emf E2​. The internal resistances of the two batteries are r1​ and r2​, respectively.

E2​r1​>E1​(R+r2​)

E1​r2​>E2​(R+r1​)

E2​r2​>E1​(R+r2​)

E1​r1​>E2​(R+r1​)