Question

Two cells of emf 1.5v and 2.0v have internal resistances 0.2$\Omega$ and 0.3$\Omega$ respectively are connected in parallel. Calculate the emf and internal resistance of the equivalent cell?

Answer 1

Given : $E_1=1.5V$ $E_2=2.0V$ $r_1=0.2\Omega$ $r_2=0.3\Omega$

Equivalent resistance of parallel combination : $\frac{1}{r_{eq}}=\frac{1}{r_1}+\frac{1}{r_2}$

$\therefore$ $\frac{1}{r_{eq}}=\frac{1}{0.2}+\frac{1}{0.3}=\frac{0.2+0.3}{0.2\times 0.3}$

$⟹$ $r_{eq}=0.12\Omega$

Equivalent Emf $E_{eq}=[\frac{E_1}{r_1}+\frac{E_2}{r_2}]r_{eq}$

$\therefore$$E_{eq}=[\frac{1.5}{0.2}+\frac{2.0}{0.3}]\times 0.12$

$E_{eq}=[7.5+6.67]\times 0.12=1.7V$