Ohm’s law and electric circuits

This chapter considers various simple dc and ac circuits which contain at least one active element (always a voltage source) and passive elements (resistors, capacitors and inductors) arranged in different combinations to form a bilateral network. The notions of complex voltage, complex current and complex impedance are introduced and then used in the ensuing analysis. Some standard ‘network theorems’ including Kirchhoff’s rules, the delta-star transformation, Thevenin’s theorem and the superposition theorem are employed. Included in the questions are circuits involving bridges, filters, audio amplifiers and transformers. Important topics such as series and parallel resonance in LRC circuits are also considered along the way. Much of the laborious algebra involved in manipulating the complex quantities above is avoided by relegating this task to Mathematica.