In the circuit shown, the initial voltages across the capacitors C₁ and C₂ are 1 V and 3 V, respectively. The switch is closed at time t = 0. The total energy dissipated (in Joules) in the resistor R until steady state is reached is _______________.

In the circuit shown, the Norton equivalent resistance (in Ω) across terminals a–b is ___________.

Let x(t) = a s(t) +s(-t) with s(t) = $$\beta {e^{ - 4t}}u\left( t \right)$$, where u(t) is unit step function. If the bilateral Laplace transform of x(t) is $$$X\left( S \right)\, = {{16} \over {{S^2} - 16}} - 4 < {\mathop{\rm Re}\nolimits} \left\{ s \right\} < 4;$$$

Then the value of β is ______.

Two casual discrete-time signals $$x\left[ n \right]$$ and $$y\left[ n \right]$$ =$$\sum\limits_{m = 0}^n x \left[ m \right]$$. If the z-transform of y$$\left[ n \right]$$=$${2 \over {z{{(z - 1)}^2}}}$$ , the value of $$x\left[ 2 \right]$$ is _____________________