Find the current in $10 \mathrm{\Omega }$ resistance, $V_1$, and source voltage $V_s$ in the circuit shown in figure. $(V_{\mathit{s}}=V_{\mathit{A}}–V_{\mathit{B}})$

All resistance in diagram (figure) are in ohms. Find the effective resistance between the points $A \text{and} B.$ 

In the given circuit determine 

$\left(\mathrm{a}\right)$ Equivalent resistance (Including internal resistance).

$\left(\mathrm{b}\right)$ Current in each resistance

$\left(\mathrm{c}\right)$ Potential difference across each resistance

$\left(\mathrm{d}\right)$ The rate at which the chemical energy of the cell is consumed

$\left(\mathrm{e}\right)$ The rate at which heat is generated inside the battery

$\left(\mathrm{f}\right)$ Electric power output

$\left(\mathrm{g}\right)$ Potential difference across battery

$\left(\mathrm{h}\right)$ Resistor that consumes maximum power out of three```````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````

$\left(\mathrm{i}\right)$Power dissipated in $3\mathrm{\Omega }$ Resistance.

In given circuit determine

$\left(\mathrm{a}\right)$ Equivalent resistance (Including internal resistance).

$\left(\mathrm{b}\right)$ Current $i, i_1, i_2$ and $i_3$.

$\left(\mathrm{c}\right)$ The potential difference across battery and each resistance.

$\left(\mathrm{d}\right)$ The rate at which the chemical energy of the cell is consumed.

$\left(\mathrm{e}\right)$ The rate at which heat is generated inside the battery.

$\left(\mathrm{f}\right)$ Electric power output.

$\left(\mathrm{g}\right)$ Which resistance consumes maximum power?

$\left(\mathrm{h}\right)$ Power dissipated across $4 \mathrm{\Omega }$ resistance.

$\left(\mathrm{a}\right)$ Determine the potential difference between $X$ and $Y$  in the circuit shown in the figure. 

$\left(\mathrm{b}\right)$ If intermediate cell has internal resistance$r=1 \mathrm{\Omega }$ then determine the potential difference between $X$ and $Y$.

Find the equivalent resistance of the circuit given in figure between the following point: 

$\left(\mathrm{i}\right) \mathrm{A} \mathrm{and} \mathrm{B}$

$\left(\mathrm{ii}\right) \mathrm{C} \mathrm{and} \mathrm{D}$

$\left(\mathrm{iii}\right) \mathrm{E} \mathrm{and} \mathrm{F}$

$\left(\mathrm{iv}\right) \mathrm{A} \mathrm{and} \mathrm{F}$

$\left(\mathrm{v}\right) \mathrm{A} \mathrm{and} \mathrm{C}$

An infinite ladder network of resistance is constructed with$1 \mathrm{\Omega }$ and $2 \mathrm{\Omega }$ resistance, as shown in the figure. 

$\left(\mathrm{i}\right)$ Show that the effective resistance between $A$ and $B$ is $2 \mathrm{\Omega }.$
$\left(\mathrm{ii}\right)$ What is the current that passes through the $2 \mathrm{\Omega }$ resistance nearest to the battery?