$n$ identical cells, each of emf $E$ and internal resistance $r$, are connected in series to a cell $A$ which is joined with reverse polarity. The potential difference across each cell, except $A$, is

In the following diagram, the potential difference between the points $\mathrm{A} \mathrm{and} \mathrm{B}$ is $\mathrm{V}$ Find an expression for the total current. Show that.

$\mathrm{V}=\frac{{\mathrm{E}}_1 {\mathrm{r}}_1+{\mathrm{E}}_2 {\mathrm{r}}_2}{{\mathrm{r}}_1+{\mathrm{r}}_2}-\mathrm{I}\frac{{\mathrm{r}}_1 {\mathrm{r}}_{}}{{\mathrm{r}}_1+{\mathrm{r}}_3}$

Calculate the net emf across $\mathrm{A}$ and $\mathrm{B}$ shown in Figure $\mathit{1}$ below$:$

Two cells of emf $2E$ and $E$ with internal resistance $r_1$and $r_2$ respectively are connected in series to an external resistor $R$ (see figure). The value of $R,$ at which the potential difference across the terminals of the first cell becomes zero is

What is the time $t$ taken by the capacitor in the given circuit to charge to $\frac{1}{\sqrt{2\pi }}$ of its full capacity?

Six cells, each of emf $5\mathrm{V}$ and internal resistance $0.1\mathrm{\Omega }$ are connected as shown in Figure. The reading of the ideal voltmeter $\mathrm{V}$ is

The current '$i$' in the circuit shown in the figure is

In the circuit diagram shown in figure given below, the current flowing through resistance $3 \mathrm{\Omega }$ is $\frac{x}{3} \mathrm{A}$. The value of $x$ is ________.

Two cells are connected between points $A$ and $B$ as shown. Cell 1 has emf of $12 \mathrm{V}$ and internal resistance of $3 \mathrm{\Omega }$. Cell 2 has emf of $6 \mathrm{V}$ and internal resistance of $6 \mathrm{\Omega }$. An external resistor $R$ of $4 \mathrm{\Omega }$ is connected across $A$ and $B$. The current flowing through $R$ will be ______ $\mathrm{A}$.

A student is asked to connect four cells of emf $\epsilon$each and internal resistance $\mathrm{r}$ in a series helping conditions. By mistake, he connects one cell in the opposite way. What will be the effective emf and effective internal resistance :

For the circuit shown in the figure, the current $I$ will be

In the given circuit, an ideal voltmeter connected across the $10 \mathrm{\Omega }$ resistance reads $2\mathrm{ }\mathrm{V}$ . The internal resistance $r$, of each cell is: