A two $$-$$ port network, shown in Fig. is described by the following equations:
$$\eqalign{ & {{\rm I}_1} = {Y_{11}}\,\,{E_1} + {Y_{12}}\,\,{E_2} \cr & {{\rm I}_2} = {Y_{21}}\,\,{E_1} + {Y_{22}}\,\,{E_2} \cr} $$

The admittance parameters, $${Y_{11}},\,\,{Y_{12}},\,\,{Y_{21}}$$ and $${Y_{22}}$$ for the network shown are

In the resistor network shown in Fig. all resistor values are $$1\,\,\Omega .$$ $$A$$ current of $$1A$$ passes from terminal $$a$$ to terminal $$b,$$ as shown in the figure. Calculate the voltage between terminals $$a$$ and $$b.$$ [Hint: You may exploit the symmetry of the circuit].

In the circuit shown in Fig. it is found that the input $$ac$$ voltage $$\left( {{V_i}} \right)$$ and current $$i$$ are in phase. The coupling coefficient is $$K = {M \over {\sqrt {{L_1}{L_2}} }},$$ where $$M$$ is the mutual inductance between the two coils. The value of $$K$$ and the dot polarity of the coil $$P-Q$$ are

In the circuit shown in Fig. what value of $$C$$ will cause a unity power factor at the $$ac$$ source?