When a resistor $$R$$ is connected to a current source, it consumes a power of $$18$$ $$W.$$ when the same $$R$$ is connected to a voltage source having the same magnitude as the current source, the power absorbed by $$R$$ is $$4.5$$ $$W.$$ The magnitude of the current source and the value of $$R$$ are

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 $$t = 0.$$