Question

Two batteries of emf 2v and 1v of internal resistances 1ohm and 2ohm are connected in parallel the effective emf of the combination is

Answer 1

if connected in series

net resistance = 1+2+x = 3+x .......... (1)

in parallel

= 2/3+x ........... (2)

when current in same in both cases

3/3+x = [4/3][2/3+x] ........ 4/3v

in parallex=6/5 = 1.2

Answer 2

Answer:

The effective emf of the combination $=1.67 \mathrm{~V}$

Explanation:

$Let \begin{aligned}&E_{1}=2 V \\&E_{2}=1 V \\&r_{1}=1 \Omega \\&r_{2}=2 \Omega\end{aligned}$

When emf are connected in parallel then the effective emf of the combination

$\frac{1}{r}=\frac{1}{r_{1}}+\frac{1}{r_{2}}$

Substitute the values

$\frac{1}{r}=1+\frac{1}{2}=\frac{2+1}{2}=\frac{3}{2}$

$r=\frac{2}{3} \\\\ \frac{E}{r}=\frac{E_{1} r_{2}+E_{2} r_{1}}{r_{1} r_{2}}$

Substitute the values

$&E \times \frac{3}{2}=\frac{2 \times 2+1 \times 1}{2} \\&E=\frac{2}{3} \times \frac{5}{2}\\=\frac{5}{3}\\=1.67 \mathrm{~V}\end{aligned}$

Hence, the effective emf of the combination $=\mathbf{1 . 6 7} \mathbf{V}$