The current in the circuit shown in figure is

When a periodic triangular voltage peak amplitude $$1$$ $$V$$ and frequency $$0.5$$ $$Hz$$ is applied to a parallel combination of $$1\,\Omega $$ resistance and $$1$$ $$F$$ capacitance, the current through the voltage source has wave-form

In the given circuit, the capacitor is initially charged to $$12$$ $$V. $$ Find the mathematical expression for the voltage across the capacitor $${{V_C}}$$ after closing the switch at $$t = 0.$$

A rectangular voltage pulse of magnitude $$V$$ and duration $$T$$ is applied to a series combination of resistance $$R$$ and capacitance $$C.$$ The maximum voltage developed across the capacitor is