The circuit shown Fig. is equivalent to a load of

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

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

Currents $${{\rm I}_1},\,{{\rm I}_2}$$ and $${{\rm I}_3}$$ meet at a junction (node) in a circuit. All currents are marked as entering the node. If $${{\rm I}_1} = - 6\sin \left( {\omega t} \right)$$ $$mA$$ and $${{\rm I}_2} = 8\cos \,\left( {\omega t} \right)\,mA,$$ then $${{\rm I}_3}$$ will be