In the following figure, C₁ and C₂ are ideal capacitors. C₁ has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is.

The average power delivered to an impedance $(4-j 3) \Omega$ by a current $5 \cos (100 \pi t+100) A$ is

If $$x\left[ n \right]$$= $${(1/3)^{\left| n \right|}} - {(1/2)^n}u\left[ n \right]$$, then the region of convergence (ROC) of its Z- transform in the Z-plane will be

The input x(t) and output y(t) of a system are related as y(t) = $$\int\limits_{ - \infty }^t x (\tau )\cos (3\tau )d\tau $$.

The system is