In the given circuit,$a$ is an arbitrary constant. The value of $m$ for which the equivalent circuit resistance is minimum is given by $\sqrt{\frac{x}{2}}$. The value of $x$ is:

Consider the circuit shown below where all resistors are $1 \,k\Omega$. If a current of magnitude $1 \,mA$ flows through the resistor marked $X$,the potential difference measured between points $P$ and $Q$ is ..............$V$.

Consider the ladder network shown in the figure. What should be the value of resistance $R$ so that the effective resistance between $A$ and $B$ becomes independent of the number of elements in the combination? ............. $\Omega$

In the circuit diagram shown,each resistor has a resistance of $1\,\Omega$. Find the equivalent resistance between $A$ and $B$.

There are three resistance coils of equal resistance. The maximum number of distinct equivalent resistances you can obtain by connecting them in any manner you choose,being free to use any number of the coils in any way,is

$A$ wire of resistance $R$ is cut into $n$ equal parts. These parts are then connected in parallel. The equivalent resistance of the combination will be