The effective resistance between $A$ and $B$ of the shown network,where the resistance of each resistor is $R$,is

If $X, Y$ and $Z$ in the figure are identical lamps,which of the following changes to the brightness of the lamps occur when switch $S$ is closed?

Three voltmeters,all having different internal resistances,are connected as shown in the figure. When a potential difference is applied across $A$ and $B$,their readings are $V_1, V_2$,and $V_3$. Choose the correct option.

$A$ current of $6\, A$ enters at corner $P$ of an equilateral triangle $PQR$ having $3$ wires of resistance $2 \,\Omega$ each and leaves by the corner $R$. The current $i_{1}$ in ampere is ........ .

$A$ battery of $emf$ $10\,V$ is connected to resistances as shown in the figure. The potential difference between $A$ and $B$,$(V_A - V_B)$ is ................ $V$.

In the circuit shown,the reading of the ammeter (ideal) is the same with both switches open as with both closed. Find the value of resistance $R$ in $\Omega$.