Examples of circuit in the following topics:
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Different Types of Currents
- A resistive circuit is a circuit containing only resistors and ideal current and voltage sources.
- If a capacitor or inductor is added to a DC circuit, the resulting circuit is not, strictly speaking, a DC circuit.
- This solution gives the circuit voltages and currents when the circuit is in DC steady state.
- A set of example circuit elements and their associated symbols commonly used in circuit diagrams.
- Describe structure of an electrical circuit and identify elements of a direct current circuit
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Introduction and Importance
- Kirchhoff's circuit laws are two equations that address the conservation of energy and charge in the context of electrical circuits.
- Kirchhoff's laws are extremely important to the analysis of closed circuits.
- However, using Kirchhoff's rules, one can analyze the circuit to determine the parameters of this circuit using the values of the resistors (R1, R2, R3, r1 and r2).
- Thus, although this law can be applied to circuits containing resistors and capacitors (as well as other circuit elements), it can only be used as an approximation to the behavior of the circuit when a changing current and therefore magnetic field are involved.
- Describe relationship between the Kirchhoff's circuit laws and the energy and charge in the electrical circuits
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RLC Series Circuit: At Large and Small Frequencies; Phasor Diagram
- From the equation, we studied resonance conditions for the circuit.
- When $Z \approx X_L$, the circuit is almost equivalent to an AC circuit with just an inductor.
- When $Z \approx X_C$, the circuit is almost equivalent to an AC circuit with just a capacitor.
- A series RLC circuit: a resistor, inductor and capacitor (from left).
- Distinguish behavior of RLC series circuits as large and small frequencies
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Combination Circuits
- A combination circuit can be broken up into similar parts that are either series or parallel.
- Combination circuit can be transformed into a series circuit, based on an understanding of the equivalent resistance of parallel branches to a combination circuit.
- A series circuit can be used to determine the total resistance of the circuit.
- In this combination circuit, the circuit can be broken up into a series component and a parallel component.
- Describe arrangement of resistors in a combination circuit and its practical implications
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Current and Voltage Measurements in Circuits
- To understand how to measure current and voltage in a circuit, you must also have a general understanding of how a circuit works and how its electrical measurements are related.
- Using this equation, we can calculate the current, voltage, or resistance in a given circuit.
- For example, if we had a 1.5V battery that was connected in a closed circuit to a lightbulb with a resistance of 5Ω, what is the current flowing through the circuit?
- A simple electric circuit made up of a voltage source and a resistor
- Describe the relationship between the electrical current, voltage, and resistance in a circuit
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Power
- Power delivered to an RLC series AC circuit is dissipated by the resistance in the circuit, and is given as $P_{avg} = I_{rms} V_{rms} cos\phi$.
- As seen in previous Atoms, voltage and current are out of phase in an RLC circuit.
- Power delivered to an RLC series AC circuit is dissipated by the resistance alone.
- The circuit is analogous to the wheel of a car driven over a corrugated road, as seen in .
- Phasor diagram for an RLC series circuit.
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Resonance in RLC Circuits
- To study the resonance in an RLC circuit, as illustrated below, we can see how the circuit behaves as a function of the frequency of the driving voltage source.
- $\nu_0$ is the resonant frequency of an RLC series circuit.
- The receiver in a radio is an RLC circuit that oscillates best at its $\nu_0$.
- The peak is lower and broader for the higher-resistance circuit.
- An RLC series circuit with an AC voltage source. f is the frequency of the source.
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Impedance
- Impedance is the measure of the opposition that a circuit presents to the passage of a current when a voltage is applied.
- Rather than solving the differential equation relating to circuits that contain resistors and capacitors, we can imagine all sources in the circuit are complex exponentials having the same frequency.
- For an RC circuit in , the AC source driving the circuit is given as:
- In the case of the circuit in , to find the complex impedance of the RC circuit, we add the impedance of the two components, just as with two resistors in series: $Z = R + \frac{ 1}{j \omega C}$.
- For a series RC circuit, we get $Z = \sqrt{R^2+(\frac{1}{\omega C})^2}$.
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Resistors in AC Circuits
- In a circuit with a resistor and an AC power source, Ohm's law still applies (V = IR).
- It is the steady state of a constant-voltage circuit.
- If the source varies periodically, particularly sinusoidally, the circuit is known as an alternating-current circuit.
- Ohm's law applies to AC circuits as well as to DC circuits.
- Apply Ohm's law to determine current and voltage in an AC circuit
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Resisitors in Series
- Most circuits have more than one component, called a resistor, that limits the flow of charge in the circuit.
- The total resistance in the circuit is equal to the sum of the individual resistances, since the current has to pass through each resistor in sequence through the circuit.
- Therefore, for every circuit with N number of resistors connected in series:
- A brief introduction to series circuit and series circuit analysis, including Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL).
- Calculate the total resistance in the circuit with resistors connected in series