Question

Two cells of emf's 1.25V and 0.75V having equal internal resistance are connected in parallel. The effective emf is

• A. 0.75V
• B. 1.25V
• C. 2.0V
• D. 1.0V
• E. 0.5V

Answer 1

Answer: (D)

1.0V

Let, Emf of one cell is $E_1=1.25V$,
Emf of other cell is $E_2=0.75V$
'$r$' be the internal resistance of both the cells,
$r=r_1=r_2$ ......................(since, both the cells have equal internal resistance)
Both the cells are connected in parallel, hence the effective emf is
$E_{eff}=\frac{E_1}{r_1}+\frac{E_2}{r_2}$

$E_{eff}=\frac{E_1{r}_2+E_2{r}_1}{r_1+r_2}$

$E_{eff}=\frac{E_{1}r+E_{2}r}{r+r}$

$E_{eff}=r\frac{E_1+E_2}{2r}$

$E_{eff}=\frac{E_1+E_2}{2}$

$E_{eff}=\frac{1.25+0.75}{2}$
$E_{eff}=\frac{2}{2}=1V$