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10.4.2: Series Impedance
https://eng.libretexts.org/Workbench/Introduction_to_Circuit_Analysis/08%3A_AC_Signal_Fundamentals/8.05%3A_Reactance_and_Impedance/10.4.2%3A_Series_Impedance
Thus, the impedance in rectangular form is the sum of the resistive components for the real portion, plus the sum of the reactances for the imaginary ( $j$ ) portion. By copying the $X_L$ vector and...Thus, the impedance in rectangular form is the sum of the resistive components for the real portion, plus the sum of the reactances for the imaginary ( $j$ ) portion. By copying the $X_L$ vector and then shifting it down and next to $X_C$ , the difference between the two reactive components can be seen (purple component directly above the $X_L$ copy).
10.3: Phasor and Complex Numbers
https://eng.libretexts.org/Workbench/Introduction_to_Circuit_Analysis/08%3A_AC_Signal_Fundamentals/8.04%3A_Complex_Numbers
Note that this is the same thing as plotting the phasor on the complex plane, and then observing the projection of the phasor on the real axis, as the phasor rotates around at a rate $\omega t$ as s...Note that this is the same thing as plotting the phasor on the complex plane, and then observing the projection of the phasor on the real axis, as the phasor rotates around at a rate $\omega t$ as shown in Figure $\PageIndex{3}$ . This can be visualized as a right triangle where the magnitude is the hypotenuse, the angle is the rotation above or below the horizontal, the horizontal component is the side adjacent to the angle and the vertical component is the side opposite of the angle.
8.1: Introduction
https://eng.libretexts.org/Workbench/Introduction_to_Circuit_Analysis/09%3A_Parallel_RLC_Circuits/9.01%3A_Introduction
The behavior of an RLC circuit can be described by Kirchhoff's voltage law (KVL) and Kirchhoff's current law (KCL), leading to differential equations that govern the dynamics of the circuit. For examp...The behavior of an RLC circuit can be described by Kirchhoff's voltage law (KVL) and Kirchhoff's current law (KCL), leading to differential equations that govern the dynamics of the circuit. For example, the voltage across the capacitor and the current through the inductor can be described by second-order differential equations, which arise from the relationships between voltage, current, and the derivative of charge or magnetic flux.
5.11.3: Differentiators
https://eng.libretexts.org/Workbench/Introduction_to_Circuit_Analysis/05%3A_Advanced_Topic-_Operational_Amplifiers/5.11%3A_Integrators_and_Differentiators/5.11.03%3A_Differentiators
First, note that the input frequency is well within the useful range of this circuit, as calculated in Example $\PageIndex{1}$ . (Note that the highest harmonics will still be out of range, but the e...First, note that the input frequency is well within the useful range of this circuit, as calculated in Example $\PageIndex{1}$ . (Note that the highest harmonics will still be out of range, but the error introduced will be minor.) The resulting DC potential is proportional to the position of the core, and thus, proportional to the position of the object under measurement.
7.7: Summary
https://eng.libretexts.org/Workbench/Introduction_to_Circuit_Analysis/07%3A_1st_Order_RC_RL_Circuit/7.07%3A_Summary
The inductor is a device that stores energy in the form of a magnetic field. Inductance is directly proportional to the permeability of the core material and the cross sectional area of the loops, and...The inductor is a device that stores energy in the form of a magnetic field. Inductance is directly proportional to the permeability of the core material and the cross sectional area of the loops, and inversely proportional to the length of the coil. It is also proportional to the square of the number of loops. The amount of time required to reach steady-state is five time constants, where one time constant is defined as the inductance divided by the circuit's effective resistance.
5.10: Basic Op Amp Circuits
https://eng.libretexts.org/Workbench/Introduction_to_Circuit_Analysis/05%3A_Advanced_Topic-_Operational_Amplifiers/5.10%3A_Basic_Op_Amp_Circuits
Relate each op amp circuit back to its general feedback form. Detail the general op amp circuit analysis idealizations. Solve inverting and noninverting voltage amplifier circuits for a variety of par...Relate each op amp circuit back to its general feedback form. Detail the general op amp circuit analysis idealizations. Solve inverting and noninverting voltage amplifier circuits for a variety of parameters, including gain and input impedance. Solve voltage/current transducer circuits for a variety of parameters. Solve current amplifier circuits for a variety of parameters. Outline the circuit modifications required for operation from a single polarity power supply.
11.5: Summary
https://eng.libretexts.org/Workbench/Introduction_to_Circuit_Analysis/11%3A_AC_Power/11.05%3A_Summary
At the other extreme, when the voltage and current are 90 degrees out of phase, as in the case of a purely capacitive or inductive load, power is alternately generated and dissipated. In between these...At the other extreme, when the voltage and current are 90 degrees out of phase, as in the case of a purely capacitive or inductive load, power is alternately generated and dissipated. In between these two extremes, that is, when the load is a complex impedance, the true power dissipation is somewhere between zero and the resistive maximum.
5.9.5: Limitations On The Use of Negative Feedback
https://eng.libretexts.org/Workbench/Introduction_to_Circuit_Analysis/05%3A_Advanced_Topic-_Operational_Amplifiers/5.09%3A_Negative_Feedback/5.9.05%3A_Limitations_On_The_Use_of_Negative_Feedback
For example, if an SP amplifier has an open-loop $Z_{in}$ of 200 k $\Omega$ and the low frequency $S$ is 500, the resulting $Z_{in}$ with feedback is 100 M $\Omega$ . The other item that must b...For example, if an SP amplifier has an open-loop $Z_{in}$ of 200 k $\Omega$ and the low frequency $S$ is 500, the resulting $Z_{in}$ with feedback is 100 M $\Omega$ . The other item that must be kept in mind is the fact that negative feedback does not change specific fundamental characteristics of the amplifier. TIMD is a function of non-linearities in the first stages of an amplifier, and the excessive application of negative feedback will not remove it.
4.1: Introduction
https://eng.libretexts.org/Workbench/Introduction_to_Circuit_Analysis/04%3A_Analysis_Theorems_and_Techniques/4.01%3A_Introduction
Once this is completed, it will be possible to convert from one type of source to another, such as creating a current source that is the functional equivalent of a voltage source. By this we mean that...Once this is completed, it will be possible to convert from one type of source to another, such as creating a current source that is the functional equivalent of a voltage source. By this we mean that if we swap one for the other in any circuit, the remainder of the circuit will behave identically, producing the same component voltage drops and branch currents.
5.9.4: The Four Variants of Negative Feedback
https://eng.libretexts.org/Workbench/Introduction_to_Circuit_Analysis/05%3A_Advanced_Topic-_Operational_Amplifiers/5.09%3A_Negative_Feedback/5.9.04%3A_The_Four_Variants_of_Negative_Feedback
Using the LF411 op amp, the high gain version shows a THD of 0.09%. Reducing the gain by a factor of 10 (and thus increasing sacrifice factor by 10 fold) yields a THD of 0.011%. Finally, a further 10 ...Using the LF411 op amp, the high gain version shows a THD of 0.09%. Reducing the gain by a factor of 10 (and thus increasing sacrifice factor by 10 fold) yields a THD of 0.011%. Finally, a further 10 fold reduction of gain yields a THD of 0.001%. Although the reduction in distortion is not exactly a factor of 10 each time, the trend can be seen clearly.
12.1: Laplace Transform
https://eng.libretexts.org/Workbench/Introduction_to_Circuit_Analysis/12%3A_Laplace_Transform_in_Circuit_Analysis/12.01%3A_Laplace_Transform
Describes Laplace transforms.

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