For what value of $R$ in circuit, current through $4\Omega$ resistance is zero?

  

At what value of the resistance $R_x$ in the circuit shown in figure will the total resistance between points $A$and $B$ be independent of the number of loops? [Given : $R=(\sqrt{3}+1)$]

All batteries are having emf $10$ volt and internal resistance negligible. All resistors are in ohms. Calculate, the current in the right most $2\Omega$ resistor.

Find current in the branch $CD$ of the circuit (in ampere).

Relation between current in conductor and time is shown in figure. If resistance of conductor is $R=3\Omega$ then find total heat dissipated (in $J$) across resistance $R$.

Find the current (in $A$) through $\frac{2}{3}\Omega$ resistance in the figure shown.

An electrical circuit is shown in figure. Calculate the potential difference (in $V$ ) across the resistor of $400\Omega$ as will be measured by the voltmeter $V$ of resistance $400\Omega$.

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)