Question

Two cells of emf 2V and 4V respectively and internal resistance 1Omega each are connected in series with emf in opposite sense.The equivalent emf of the combination is ?​

Answer 1

Given:

Two cells of emf 2V and 4V respectively and internal resistance 1Omega each are connected in series with emf in opposite sense.

To find:

Net EMF of combination?

Calculation:

Since the cells are connected in series combination, we can say:

$\rm EMF_{net} = 4 - 2 = 2 \: volt$

Now, the net internal resistance will be :

$\rm r_{int} = 10 + 10 = 20 \: ohm$

So, the equivalent battery is :

2 volt battery with internal resistance of 20 ohm.

Answer 2

$\sf\huge\bold{Answer:}$

Given :

Emf of 1st cell$\tt {(ε_{ 1} )}$ = 2V

Emf of 2nd cell$\tt {(ε_{ 2})}$  = 4V

Internal resistance of 1st cell ($r_1$) = 1Ω

Internal resistance of 2st cell ($r_2$) = 1Ω

Cells are connected in series

To find :

Equivalent emf of the series combination formed by 2 cells.

Solution :

When cells are in series, emf of cells subtract to give equivalent emf.

$\fbox{Formula used :}$

$\tt\bold \red{ε_{ eq} = ε_{2} - ε_{ 1},} (when \: ε_{2} > ε_{1}).$

$\tt\bold {:⟶ε_{ eq} = 4V- 2V}$

$\tt\bold {:⟶ε_{ eq} = 2V}$

$\bf\huge\purple {ε_{ eq} = 2V}$

Let's know more :

When cells are in series, internal resistance of cells add up to give total internal resistance:

$\fbox{Formula used :}$

$\tt\bold \red{r_{ int} = r_{1} + r_{ 2}}$

$\tt \bold{:⟶r_{ int} =  1Ω+ 1Ω}$

$\tt\bold {:⟶r_{ int} =  2Ω}$

$\bf\huge\purple {r_{ int} =  2Ω}$