Let us now define resonance. In a two-terminal electrical network containing at least one inductor and one capacitor, resonance is the condition which exists when the input impedance of the network is purely resistive

Example 1: If 0=4v2 cos\tV, Z=2/600Q2 Find p(t)and P. Solution:

8-1 Nodal, mesh and loop analysis Nodal analysis:

A real, an imaginary, or a complex forcing function will produce a real, an imaginary, or complex response, respectively. Instead of applying a real forcing function to obtain the desired real response, we apply a complex forcing function whose real part is the given real forcing function; we obtain a complex response whose real part is the desired real response

The complete response is written as the sum of the forced and the natural response, and the initial conditions are then determined and applied to the complete response to find the values of the constants

The complete response of any RC circuit may also be obtained as the sum of the natural and the forced response

4-5 Simple capacitor-OP-AMP-circuits Integrator op-amp circuit (Integrator):

A current-carrying conductor produced a magnetic field (1800). A changing magnetic field could induce a voltage in a neighboring circuit(1820)

The operational amplifier (hereafter OP-AMP)is developed in the 1940s primarily for use in analog computers, made cheaply and readily available in the late 1960s through integrated-circuit technology. The actual construction of a modern OP-AMP is indeed very complex, involving many transistors, diodes, resistors and capacitors

Mesh analysis is applicable only to those networks, which are planar. If it is possible to draw the diagram of a circuit on a plane surface in such a way that no branch passes over or under any other branch, then that circuit is said to be planar circuit. (Non-planar-circuit