Impedance, Z, is the "resistance" or opposition to the flow of alternating current. It is the algebraic sum of a purely resistive term, R, and a purely reactive term, X. Both R and X are measured in ohms but they are quite different. The reactive term is a function of frequency; by definition, the resistive term is not. You can take Ohm's Law, E = IR, and replace R with Z. However, it then gets more complicated because Z is generally a complex number composed of a "real" part (the resistance) plus an "imaginary" part (the reactance). That's really a confusing way to say that the sinusoidal current is not in phase with the sinusoidal voltage if the "imaginary" part is non-zero. If the "imaginary" part is zero, then Z = R (pure non-reactive resistance) and we don't need to call it impedance. Impedance is only valid for non-DC situations.
Real circuits are never purely DC. Even a simple dry cell connected with a switch to a "pure" resistance will exhibit a finite turn-on and turn-off time because of wire inductance and stray capacitance in a circuit made with real components. So, when DC is replaced by AC, complex arithmetic (the arithmetic of complex numbers) is needed to understand what is going on.
Both inductance and capacitance oppose the flow of alternating current, but in different ways. The opposition to the flow of alternating current in inductors and capacitors is called reactance. Reactance is always associated with the storage of electrical energy in either a magnetic field (inductors) or an electrostatic field (capacitors). For pure sinusoidal AC of fixed frequency, inductive reactance, XL in ohms is +j (2πfL) and capacitive reactance, XC in ohms is -j 1/(2πfC), where j is the "imaginary" operator equal to √-1, f is frequency in hertz, L is inductance in henries, and C is capacitance in farads.
In computing the reactance of a circuit, the capacitive reactance subtracts from the inductive reactance leaving either a +j or a -j term in the difference. Note that inductive reactance increases both with increasing frequency and increasing inductance while capacitive reactance decreases with both increasing frequency and increasing capacitance. So, for any given (fixed) values of inductance and capacitance, there will be a frequency where the inductive reactance is exactly equal to the capacitive reactance, there is no "imaginary" term to the impedance, and the circuit is said to be resonant at the frequency for which that occurs. All that means is the electrical energy is sloshing back and forth between the inductance and the capacitance with no net change of energy stored in the circuit.
All the above comes from very basic AC circuit theory, but it can take awhile to really get a "feel" for what is going on. I found that plotting the Xs and Rs on a graph with vertical X and a horizontal R axes was helpful. You can then use geometry to "sum" X values with R values to arrive at a "vector sum" whose length is the magnitude of the impedance, Z. Or use this formula: |Z| = √(R2 + X2). Note that Z is generally complex, so the formula only gives the magnitude of Z; there is also a "phase angle" associated with Z
As for op-amps... the input impedance of an op-amp is affected by the circuit it is in. For initial rule-of-thumb calculations, "ideal" op-amps have infinite input impedance, zero output impedance, infinite gain, and infinite bandwidth. The infinite input impedance means the op-amp draws no current when a signal is applied between the inverting input and the non-inverting input. Zero output impedance means you can connect any load you want and the output will not change. Infinite gain means there is zero differential input voltage between the inverting and non-inverting inputs, which condition is achieved by external negative feedback around the op-amp. Infinite bandwidth means that circuit operation is defined only by the external components and how they are connected, not by the op-amp. There is no such thing as an "ideal" op-amp, but these conventions are useful for initial circuit design.
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