In the network shown in the following figure,each resistance is $1\,\Omega$. The effective resistance between $A$ and $B$ is

$A$ ring is made of a wire having a total resistance $R_0 = 12\,\Omega$. Find the ratio of the lengths $\frac{\ell_1}{\ell_2}$ of the two arcs between points $A$ and $B$ as shown in the figure,such that the equivalent resistance $R$ of the circuit between these points is $\frac{8}{3}\,\Omega$.

$6 \Omega$ and $12 \Omega$ resistors are connected in parallel. This combination is connected in series with a $10 \text{ V}$ battery and a $6 \Omega$ resistor. What is the potential difference between the terminals of the $12 \Omega$ resistor (in $\text{ V}$)?

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:

$A$ Copper $(Cu)$ rod of length $25 \, cm$ and cross-sectional area $3 \, mm^2$ is joined with a similar Aluminium $(Al)$ rod as shown in the figure. Find the resistance of the combination between the ends $A$ and $B$ (in $m\Omega$).
(Take Resistivity of Copper $= 1.7 \times 10^{-8} \, \Omega \cdot m$,Resistivity of Aluminium $= 2.6 \times 10^{-8} \, \Omega \cdot m$)

Find the equivalent resistance between the points $a$ and $b$ in $\Omega$.