
Circuit Theory, as the name suggests, enables a detailed mathematical study to be made of virtually any electrical circuit. This has formed the backbone of electrical study since its inception in the early 1800s, permitting engineers to design more efficient electrical apparatus.
In 1820, H.C. Oersted, from Copenhagen, discovered that the flow of electric current in a conductor would cause a magnetic field, thereby producing a deflection of a compass needle. This discovery led to research in the field of electromagnetics, the interaction between electricity and magnetism, an early pioneer of which was the Frenchman A.M. AmpÃ¨re. AmpÃ¨re gave clear definitions of electric current, the flow of electric charge in a conductor, and electric voltage, the tension of â€˜pressureâ€™ of electricity which would cause the flow of current in a closed circuit.
AmpÃ¨re, however, saw no relationship between the current and voltage, and it was G.S. Ohm in 1827 who finally postulated that voltage was proportional to the current by a constant known as the resistance of the conductor. An analogy may be made between electricity and water flow in a pipe. Greater water pressure, or voltage, is required to overcome the resistance of the pipe, or conductor, to increase the water flow, or current.
Such was the impact of Ohm\'s Law that the main pioneers have been honoured by using their names as the terms of resistance and current. Current (I) is measured in units of AmpÃ¨res and resistance (R) is measured in Ohms. If the voltage applied is V Ohm\'s law is written as I = V/R.
Following Ohm\'s Law and the recognition of resistance and the role it played, further circuit laws soon appeared. In 1841, J.P. Joule discovered that the rate of heating (P), expressed as Watts, produced by an electric current (I) flowing in a conductor of known resistance (R) was equal to the current in ampÃ¨res squared times the resistance: P = I2R.
Electrical engineering and the design and analysis of electrical circuits using circuit theory can be traced back to 1848, when G. Kirchoff discovered the current and voltage laws, subsequently named after him. Kirchoff applied Ohm\'s Law to circuits having several components and found that the sum of the currents at an interconnected point equalled zero, and that the sum of the voltages around a closed loop of the circuit equalled zero.
Including Kirchoff\'s Laws elementary circuit theory was essentially complete following the discovery of two other electrical concepts, capacitance and inductance, and their effect on the circuit behaviour. Capacitance relates to the ability of a condenser to store energy, and induction to a characteristic of electrical coils to resist rapidly changing currents. These concepts are necessary to analyse circuits in which the power supply is alternating, that is, varying at a fixed frequency between positive and negative (i.e. the direction of flow of current flow reverses in every cycle). William Thomson is credited with realizing the importance of capacitance through work on improving undersea cables, and Oliver Heaviside with inductance after early work with telegraphy.
From these early beginnings circuit theory now extends, through the application of network theory, to the analysis and design of the most complicated circuits, for instance those in computer silicon â€˜chipsâ€™. AC 
