Consider the circuit shown in Fig. If the frequency of the source is $$50$$ $$Hz,$$ then a value of $${t_0}$$ which results in a transient free response 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 $$0.25?$$

The graph of an electrical network has $$N$$ nodes and $$B$$ branches. The number of links, $$L$$, with respect to the choice of a tree, is given by

An electrical network is fed by two $$ac$$ sources, as shown in Fig. Given that
$${Z_1} = \left( {1 - j} \right)\Omega ,\,\,{Z_2} = \left( {1 + j} \right)\Omega $$ and $${Z_L} = \left( {1 + j0} \right)\Omega .$$ Obtain the Thevenin equivalent circuit (Thevenin voltage and impedance) across terminals $$X$$ and $$Y$$, and determine the current $${{\rm I}_L}$$ through the load $${Z_L}.$$