Q136 / 170 · Manipal (MET) 2015 · Physics

Under what conditions 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
    $E_2 r_1 \gt E_1\left(R+r_2\right)$
  • Correct answer
    B
    $E_1 r_2 \lt E_2\left(r_1+R\right)$
  • C
    $E_2 r_2 \lt E\left(R+r_2\right)$
  • D
    $E_1 r_1 \gt E_2\left(r_1+R\right)$

Solution

The current through the circuit before the battery of emf $E_2$ is short circuited, is $i_1=\frac{E_1+E_2}{r_1+r_2+R}$ ...(i) After short circuiting the battery of emf $E_2$, current through the resistance $R$ would be $i_2=\frac{E_1}{R+I_1}$ ...(ii) Since, from Eqs. (i) and (ii), we get $i_2 \gt i_1$ $\therefore \quad \frac{E_1}{R+r_1} \gt \frac{E_1+E_2}{R+r_1+r_2}$ This gives $\quad E_1 r_2 \gt E_2\left(R+r_1\right)$

Hence, the correct answer is option: 'B'.

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