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

The effective inductance of the circuit across the terminals $$A,B$$ in the Figure shown below is

A $$10$$ $$V$$ battery with an internal resistance of $$1\,\Omega $$ is connected across a nonlinear load whose $$V-1$$ characteristic is given by $$7{\rm I} = {V^2} + 2V.$$ The current delivered by the battery is ............... $$A.$$