$A$ wire of resistance $R$ is divided into $10$ equal parts. These parts are connected in parallel. The equivalent resistance of such a connection will be: (in $, R$)

In the given figure,$R_1=10 \Omega, R_2=8 \Omega, R_3=4 \Omega$ and $R_4=8 \Omega$. The battery is ideal with an emf of $12 \text{ V}$. Find the equivalent resistance of the circuit and the current supplied by the battery.

Find the net resistance between points $X$ and $Y$ for the given infinite ladder network,where each resistor has a resistance of $R$.

$(a)$ Three resistors $1 \;\Omega, 2 \;\Omega$ and $3 \;\Omega$ are combined in series. What is the total resistance of the combination?
$(b)$ If the combination is connected to a battery of $emf \; 12 \; V$ and negligible internal resistance,obtain the potential drop across each resistor.

The equivalent resistance between $A$ and $B$ is: (in $\Omega$)

Three resistances of magnitude $2\,\Omega$,$3\,\Omega$,and $5\,\Omega$ are connected in parallel to a battery of $10\,V$ and of negligible resistance. The potential difference across the $3\,\Omega$ resistance will be ............... $V$.