In the given circuit,if $E_1 = 4\,V$,$R_1 = 2\,\Omega$,$E_2 = 6\,V$,$R_2 = 2\,\Omega$,and $R_3 = 4\,\Omega$,what is the value of current $i_1$ in $A$?

In the ladder network shown, the current through the resistor $3\, \Omega$ is $0.25\, A$. The input voltage $V$ is equal to: (in $V$)

In the circuit shown,the galvanometer $G$ of resistance $60 \, \Omega$ is shunted by a resistance $r = 0.02 \, \Omega$. The current through $R$ is nearly $1 \, A$. The value of resistance $R$ (in $\Omega$) is nearly:

Three resistors $1 \Omega, 2 \Omega$ and $3 \Omega$ are connected to form a triangle. Across the $3 \Omega$ resistor,a $3 \text{ V}$ battery is connected. The current through the $3 \Omega$ resistor is: (in $\text{ A}$)

Two cells of $e.m.f.$ $E_1$ and $E_2$ and of negligible internal resistances are connected with two variable resistors as shown in the figure. When the galvanometer shows no deflection,the values of the resistances are $P$ and $Q$. What is the value of the ratio $E_2/E_1$?

An electrical circuit consists of ten $100 \,\Omega$ resistors. Out of these $10$ resistors,a group of $n_1$ resistors are connected in parallel and another group of $n_2$ resistors are separately connected in parallel. These two groups are then connected in series and this combination is connected to a voltage source of $100 \,V$. If the net current through the circuit is $2.5 \,A$,the values of $n_1$ and $n_2$ are: