# Integrals & Trig Functions

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### Find the Total Response of a Series RC Circuit

After finding the zero-input response and the zero-state response of an RC series circuit, you can easily find the total response of the circuit. Remember that a first-order RC series circuit has one resistor

### Analyze a Parallel RL Circuit Using a Differential Equation

A first-order RL parallel circuit has one resistor (or network of resistors) and a single inductor. First-order circuits can be analyzed using first-order differential equations. By analyzing a first-order

### Find the Zero-State Response of a Parallel RL Circuit

A first-order RL parallel circuit has one resistor (or network of resistors) and a single inductor. First-order circuits can be analyzed using first-order differential equations. By analyzing a first-order

### Find the Total Response of a Parallel RL Circuit

After finding the zero-input response and the zero-state response of an RL parallel circuit, you can easily find the total response of the circuit. Remember that a first-order RL parallel circuit has one

### How to Solve Differential Equations Using Op Amps

The op amp circuit can solve mathematical equations fast, including calculus problems such as differential equations. To solve a differential equation by finding

### How to Prepare an Op Amp Circuit to Do Complex Mathematics

By adding a capacitor to an operational-amplifier (op amp) circuit, you can use the op amp circuit to do more-complex mathematical operations, like integration and differentiation. Practically speaking

### Describe Circuit Inductors and Compute Their Magnetic Energy Storage

In circuits, inductors resist instantaneous changes in current and store magnetic energy. Inductors are electromagnetic devices that find heavy use in radiofrequency

### Calculate the Total Capacitance for Parallel and Series Capacitors

Capacitors store energy for later use. The capacitance is the ratio between the amount of charge stored in the capacitor and the applied voltage. Capacitance is measured in

### Find the Power and Energy of a Capacitor

Capacitors store energy for later use. The instantaneous power of a capacitor is the product of its instantaneous voltage and instantaneous current. To find the instantaneous power of the capacitor, you

### Relate the Current and Voltage of a Capacitor

Capacitors store energy for later use. The voltage and current of a capacitor are related. The relationship between a capacitor’s voltage and current define its capacitance and its power. To see how the

### How to Perform Complex Processing with Op Amps

If you understand the basic building blocks of op amp circuits, you’re ready to tackle complex processing actions with op amps. Using op amp circuits, you can analyze an instrumentation amplifier, solve

### Op Amp Circuits and Circuit Analysis

The op amp circuit is a powerful took in modern circuit applications. You can put together basic op amp circuits to build mathematical models that predict complex, real-world behavior. Commercial op amps

### Analyze Noninverting Op Amp Circuits

Use op amp circuits to build mathematical models that predict real-world behavior.The mathematical uses for signal processing include noninverting and inverting amplification. One of the most important

### Analyze Inverting Op Amp Circuits

An inverting amplifier takes an input signal and turns it upside down at the op amp output. When the value of the input signal is positive, the output of the inverting amplifier is negative, and vice versa

### Analyze a Unique Inverting Op Amp: A Summing Amplifier

You can extend an inverting amplifier to more than one input to form a summer, or summing amplifier. An inverting amplifier takes an input signal and turns it upside down at the op amp output.

### Analyze a Unique Inverting Op Amp: An Op Amp Subtractor

There’s a special op amp circuit —a differential amplifier, or subtractor — that is actually a combination of a noninverting amplifier and inverting amplifier. A differential amplifier multiplies the difference

### Find Thévenin’s and Norton’s Equivalents for Complex Source Circuit

A Thévenin or Norton equivalent circuit is valuable for analyzing the source and load parts of a circuit. Thévenin’s and Norton’s theorem allow you to replace a complicated array of independent sources

### Gauge Maximum Power Transfer Using Thévenin’s and Norton’s Theorems

Thévenin’s and Norton’s theorems can be used to analyze complex circuits by focusing on the source and load circuits. One application of Thévenin’s and Norton’s theorems is to calculate the maximum power

### Find Thévenin and Norton Equivalent Circuits Using Source Transformation

A Thévenin or Norton equivalent circuit is valuable for analyzing the source and load parts of a circuit. Thévenin’s and Norton’s theorems allow you to replace a complicated array of independent sources

### Analyze Circuits with Three Independent Sources Using Superposition

Use superposition to analyze circuits that have lots of voltage and current sources. Superposition helps you to break down complex linear circuits composed of multiple independent sources into simpler

### Analyze Circuits with Two Independent Sources Using Superposition

Use superposition to analyze circuits that have lots of voltage and current sources. Superposition helps you to break down complex linear circuits composed of multiple independent sources into simpler

### Analyze Circuits with Dependent Sources

You can analyze circuits with dependent sources using node-voltage analysis, source transformation, and the Thévenin technique, among others. For analyzing circuits that have dependent sources, each technique

### Circuit Analysis and Mesh-Current Equations

Mesh-current analysis (loop-current analysis) can help reduce the number of equations you must solve during circuit analysis. Mesh-current analysis is simply Kircholff’s voltage law adapted for circuits

### How to Work with Voltage Sources in Node-Voltage Analysis

Voltages across each device in a circuit can be described using node-voltage analysis (NVA). Node-voltage analysis reduces the number of equations you have to deal with when performing circuit analysis

### Simplify Circuit Analysis by Transforming Sources in Circuits

With transformation, you can modify a complex circuit so that in the transformed circuit, the devices are all connected in series or in parallel. By transforming circuits, you can apply shortcuts such

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