Combination of Cells

Two batteries with emf $12 \mathrm{V}$ and $13 \mathrm{V}$ are connected in parallel across a load resistor of $10 \mathrm{\Omega }$. The internal resistances of the two batteries are $1 \mathrm{\Omega }$ and $2 \mathrm{\Omega }$, respectively. The voltage across the load lies between

Find the emf and internal resistance of the equivalent cell between $A$ and $B$. Put ${\epsilon }_1=6 \mathrm{V}$, $r_1=2 \mathrm{\Omega }\text{,} {\mathrm{\epsilon }}_2=4 \mathrm{V}\text{,} r_2=2 \mathrm{\Omega }$ and ${\epsilon }_3=3 \mathrm{V}$, $r_3=3 \mathrm{\Omega }$.

$n$ identical cells are joined in series with its two cells $A$ and $B$ in the loop with reversed polarities. Emf of each shell is $\epsilon$ and internal resistance $r$. Potential difference across cell $A$ or $B$ is (here $n>4$)

What should be the value of $\frac{E_1}{E_2}$ so that current flowing through $7 \mathrm{\Omega }$ resistor could be increased by short-circuiting the battery of emf $E_2$?

A cell of emf $\epsilon$ and internal resistance $r$ is charged by a current $i$, then

To get the maximum current through a resistance of $2.5 \mathrm{\Omega }$, one can use $m$ rows of cells, each row having $n$ cells. The internal resistance of each cell is $0.5 \mathrm{\Omega }$. What are the values of $n$ and $m$, if the total number of cells is $45$?

To get maximum current through a resistance of $2.5 \mathrm{\Omega }$, one can use m rows of cells, each row having $n$ cells. The internal resistance of each cell is $0.5 \mathrm{\Omega }$. What are the values of $n$ and $m$? If the total number of cells is $45$.

$n$ identical cells, each of emf $\epsilon$ and internal resistance $r$, are joined in series to form a closed circuit. One cell $A$ is joined with reversed polarity. The potential difference across each cell is $\epsilon$, the potential difference across $A$ is,

$n$ identical cells, each of emf $\epsilon$ and internal resistance $r$, are joined in series to form a closed circuit. One cell $A$ is joined with reversed polarity. The potential difference across each cell except $A$ is,

$N$ identical cells are connected to form a battery. When the terminals of the battery are joined directly (short-circuited), current $I$ flows in the circuit. To obtain the maximum value of $I$,