A potentiometer wire $AB$ is $100 \mathrm{cm}$ long and has a total resistance of $10\mathrm{ohm}$. if the galvanometer shows zero deflection at the position $C$, then find the value of unknown resistance $R$( in $\Omega$ ).

  

In the figure shown, for given values of $R_1$ and $R_2$ the balance point for Jockey is at $40 \mathrm{cm}$ from $A$. When $R_2$ is shunted by a resistance of $10 \mathrm{\Omega }$, balance point shifts to $50 \mathrm{cm}$. Find $\left(\frac{R_1{R}_2}{3}\right) \left(\text{in} {\mathrm{ohm}}^2\right)\text{.} \left(\mathrm{AB}=1 \mathrm{m}\right)$

(Approximate the answer to two decimal place)

In the primary circuit of potentiometer for rheostat can be varied from $0$ to $10\Omega$. Initially it is at minimum resistance (zero). Now the rheostat is put at maximum resistance $\left(10\Omega \right)$ and the switch$S$ is closed. New balancing length is found to $8 \mathrm{m}$. Find the internal resistance $r$of the $4.5 \mathrm{V}$ cell.

$324$ identical galvanic cells, each of internal resistance $9\Omega$ are arranged as several in-series groups of cells connected in parallel. The arrangement has been laid out so that power output in an externally connected resistance of value $4\Omega$ is maximum. If $n$cells are connected in every series group that form parallel combination, then find value of $n$.

In given electrical circuit, let power supplied by battery $E_1$ be '$a$' watt and power supplied by battery $E_2$ ? be ' $b$ ' watt then what is the value of $a+b$.

Find the resistor in which maximum heat will be produced.

In the circuit shown in figure potential difference between point $A$ and $B$ is $16 \mathrm{V}$. Find the current (in $A$ ) passing through $2\Omega$ resistance.

For the circuit shown in figure, find

(i) the initial current through each resistor

(ii) steady state current through each resistor

(iii) final energy stored in the capacitor

(iv) time constant of the circuit when switch is closed.

(v) time constant of the circuit when switch is open

In the network shown in figure, find $I,I_1$ and the charge on the $7\mathrm{\mu F}$ capacitor after steady state condition is reached.