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].

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 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

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 $$0.25?$$