In the present paper, the Gupta transform (GT) which is a contemporary integral transform has been employed for the anatomy of a series network of an inductor (L), a resistor (R), and a capacitor (C) (i.e. a series LRC network) across which coupled a steady stimulating source of voltage, and a parallel network of an inductor (L), a resistor (R), and a capacitor (C) (i.e. a parallel LRC network) across which coupled a steady stimulating source of current. Such anatomy provides the nature of current through a series LRC network across which coupled a steady stimulating source of voltage and the nature of voltage across a parallel LRC network across which coupled a steady stimulating source of current. The nature of current through a series LRC network across which coupled a steady stimulating source of voltage and the nature of voltage across a parallel LRC network across which coupled a steady stimulating source of current, are determined by the GT with simple computations which corroborate that the GT is a puissant mathematical method for the anatomy of such series or parallel network than the other mathematical method or approach like calculus method. The nature of current through a series LRC network across which coupled a steady stimulating source of voltage and the nature of voltage across a parallel LRC network across which coupled a steady stimulating source of current, are found to depend on the values of resistance (R) inductance (L) and Capacitance (C) of the elements: resistor, inductor, and capacitor of the networks.