In the following circuit the capacitance varies as C = KQ, where K is a constant equal to 0.5 Farads/Coulomb and Q, the charge on the capacitor in Coulombs. Determine the current through the circuit and sketch the voltage waveform across the capacitor (V_C) for a step input V_i as shown in figure.

In figure, A₁, A₂ and A₃ are ideal ammeters. If A₁ reads 5 A, A₂, A₂ reads 12 A, then A₃ should read

If $$F\left( s \right) = L\left[ {f\left( t \right)} \right] = {K \over {\left( {s + 1} \right)\,\left( {{s^2} + 4} \right)}}$$ then $$\matrix{ {Lim\,f\,\left( t \right)} \cr {t \to \infty } \cr } $$ is given by

The Laplace transform of the periodioc function f(t) describe4d by the curve below, i.e., $$f\left( t \right) = \left\{ {\matrix{ {\sin \,t\,\,\,if\,\left( {2n - 1} \right)\pi \le t \le 2n\pi } \cr {0\,\,\,\,\,\,\,\,otherwise} \cr } } \right.$$
is _________. (fill in the blank), n is an integer.