Two cells of same emf but different internal resistances r 1 and r 2 are connected in series with a resistance R. The value of resistance R, for which the potential difference across second cell is zero, is

Question

Two cells of same emf but different internal resistances r 1 and r 2 are connected in series with a resistance R. The value of resistance R, for which the potential difference across second cell is zero, is (A) r 2- r 1 (B) r1-r2 (C) r 1 (D) r 2

Tardigrade Admin · Accepted Answer

I=(2 E/R+r1+r2) ldots ldots( i ) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/02bcd5effa75d7350812af876851fd6e-.png" /> But V A - V B = E - Ir 2=0 ⇒ I=(E/r2) ldots ldots( ii ) Comparing values of I from (i) and (ii) (E/r2)=(2 E/R+r1+r2) ⇒ R=r2-r1

Q. Two cells of same emf but different internal resistances $r_{1}$ and $r_{2}$ are connected in series with a resistance $R$ . The value of resistance $R$ , for which the potential difference across second cell is zero, is

$r_{2} - r_{1}$

$r_{1} - r_{2}$

$r_{1}$

$r_{2}$

$I = \frac{2 E}{R + r _{1} + r _{2}} \dots\dots (i)$

But $V_{A} - V_{B} = E - I r_{2} = 0$
$\Rightarrow I = \frac{E}{r _{2}} \dots\dots (ii)$
Comparing values of I from (i) and (ii)
$\frac{E}{r _{2}} = \frac{2 E}{R + r _{1} + r _{2}}$
$\Rightarrow R = r_{2} - r_{1}$

Q. Two cells of same emf but different internal resistances r1​ and r2​ are connected in series with a resistance R. The value of resistance R, for which the potential difference across second cell is zero, is

r2​−r1​

r1​−r2​

r1​

r2​