Solve the circuit shown in Fig. using the mesh method of analysis and determine the mesh currents $${{\rm I}_1},\,{{\rm I}_2},$$ and $${{\rm I}_3}$$. Evaluate the power developed in the $$10$$ $$V$$ voltage source.

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

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 series $$R-L-C$$ circuit when excited by a $$10$$ $$V$$ sinusoidal voltage source of variable frequency, exhibits resonance at $$100$$ $$Hz$$ and has a $$3$$ $$dB$$ bandwidth of $$5$$ $$Hz.$$ The voltage across the inductor $$L$$ at resonace is