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

A series $$R-L-C$$ circuit has $$R = 50\Omega ;$$ $$L=100$$ $$\mu H$$ and $$C = 1\,\,\mu F.$$ The lower half power frequency of the circuit is

A first order, low pass filter is given with $$R = 50\,\,\Omega $$ and $$C$$ $$ = 5\mu F.$$ What is the frequency at which the gain of the voltage transfer function of the filter is $$0.25?$$

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