Two cells of EMF $1.5\,\text{V}$ and $2.0\,\text{V}$, having internal resistances $0.2\,\Omega$ and $0.3\,\Omega$ respectively, are connected in parallel. Calculate the EMF and the internal resistance of the equivalent cell.

$E_{eq}=1.7\,\text{V}$, \; $r_{eq}=0.12\,\Omega$.

CBSE Class 12 · 2016 · Delhi · Current ElectricityShort Answer

Two cells of EMF

1.5 V

and

2.0 V

, having internal resistances

0.2 Ω

and

0.3 Ω

respectively, are connected in parallel. Calculate the EMF and the internal resistance of the equivalent cell.

Answer: $E_{e q} = 1.7 V$ , \; $r_{e q} = 0.12 Ω$ .

For cells in parallel,

E_{e q} = \frac{E _{1} / r _{1} + E _{2} / r _{2}}{1/ r _{1} + 1/ r _{2}} = \frac{1.5/0.2 + 2.0/0.3}{1/0.2 + 1/0.3} = \frac{7.5 + 6.67}{5 + 3.33} = 1.7 V,

and

r_{e q} = \frac{r _{1} r _{2}}{r _{1} + r _{2}} = \frac{0.2 \times 0.3}{0.5} = 0.12 Ω.

CBSE Class 12 Board · 2016 · Delhi · Subjective