In the given circuit,the equivalent resistance between the terminals $A$ and $B$ is $........\Omega$.

$A$ 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 $\frac{8}{3}\,\Omega$.

Two heater wires of equal length are first connected in series and then in parallel. The ratio of heat produced in the two cases is

Two resistors $R_{1} = (4 \pm 0.8) \, \Omega$ and $R_{2} = (4 \pm 0.4) \, \Omega$ are connected in parallel. The equivalent resistance of their parallel combination will be

$A$ straight wire of resistance $18 \Omega$ is bent in the form of an equilateral triangular loop. The effective resistance between any two vertices of the triangle is (in $\Omega$)

$A$ copper wire of resistance $R$ is cut into ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have a resistance