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米奇
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- 註冊時間: 週二 11月 27, 2001 8:00 am
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The International System of Units (SI) enables engineers to communicate in a meaningful way about quantitative results.
Table 1.1 summarizes the base SI units; Table 1.2 presents some useful derived Si units.
Circuit analysis is based on the variables of voltage and current.
Voltage is the energy per unit charge created by charge separation and has the SI unit of volt(v=dq/dq).
Current is the rate of charge flow and has the SI unit of ampere(i=dq/dt).
The ideal vasic circuit element is a two-terminal component that cannot be subdivided; it can be described mathematically in terms of its terminal voltage and current.
The passive sign convention uses a positive sign in the expression thatrelates the voltage and current at the terminals of an element when the reference direction for the current through the element is in the direction of the reference voltage drop across the element.
Power is energy per unit of time and is equal to the product of the terminal voltage and current; it has the SI unit of watt(p=dq/dt=vi).
The algebraic sign of power is interpreted as follows:
If P>0, power is being delivered to the circuit or circuit component.
If P<0, power is being extracted from the circuit or circuit component.
The circuit elements introduced in this chapter are voltage sources, current sources, and resistors:
An ideal voltage source maintains a prescribed voltage regardless of the current in the divice. An ideal current source maintains a presscribed current regardless of the voltage across the divice. Voltage and current sources are either voltage in the circuit; or dependent, that is, determined by some other current or voltage in the circuit.
A resistor constrains its voltage and current to be proportional to each other. The value of the proportional constant relating voltage and current in a resistor is called its resistance and is measured in ohms.
Ohm's law establishes the proportionality of voltage and current in a resistor. Specifically.
v=iR
if the current flow in the resistor is in the direction of the voltage drop across it, or v=-iR
if the current flow in the resistor is in the direction of the voltage rise across it.
Vy com bining the equation for power, p=vi, with Ohm's law, we can determine the power absorbed by a resistor;
p=i^2R=v^2/R
Circuits are described by nodes and closed paths. A node is a point where two or more circuit elements join. When just two closed path is a loop traced through connecting elements, startnodes only once each.
The voltage and currents of interconnected circuit elements obey Kirchhoff's laws:
Kirchhoff's current law states that the algebraic sum of all the currents at any node in a circuit equals zero.
Kirchhoff's valtage law states that the algebraic sum of all the voltages around any closed path in a circuit equals zero
A circuit is solved when the voltage across and the current in every element have been determined. By combining an understanding of independent and dependent sources, Ohm's law, and Kirchhoff's laws, we can solve many simple circuits.
Series resistors can be combined to obtain a single equivalent resistance according to the equation
Parallel resistors can be combined to obtain a single equivalent resistance according to the equation
When just two resistors are in parallel, the equation for equivalent resistance can be simplified to give
When voltage is divided across series resistors, as shown in the figure, the voltage across each resistor can be found according to the equations
When current is divided across parallel resistors, as shown in the figure, the current through each resistor can be found according to the equations
A voltmeter measures voltage and must be placed in parallel with the voltage being measured, An ideal voltmeter has infinite internal resistance and thus does not alter the voltage being measured.
An ammeter measures current and must be placed in series with the current being measured. An ideal ammeter has zero internal resistance and thus does not alter the current being measured.
Digital meters and analog meters have internal resistance, which influences the value of the circuit variable being measured.meters based on the d'Arsonval meter movement deliberately include internal resistance as a way to limit the current in the movement's coil.
The Wheatstone bridge circuit is used to make precise measurements of a resistor's value using four resistors,a dc voltage source, and a galvanometer.A Wheatstone bridge is balanced when the resistors obey Eq.(3.29), resulting in a galvanometer reading of 0A.
A circuit with three resistors connected in a Δ configuration(or a π configuration) can be transformed into an equivalent circuit in which the three resistors are Y connected(of T connected).The Δ-to-Y transformation is given by Eqs.(3.40)-(3.42); the Y-to-Δ transformation is given by Eqs.(3.43)-(3.45).
For the topics in this chapter,mastery of some basic terms, and the concepts they represent, is necessary. Those terms are node, planar circuit. Table 4.1 provides defiritions and examples of these terms.
Two new circuit analysis techniques were introduced in this chapter:
The node-coltage method works with both planar and nonplanar circuits. Areference node is chosen from among the essential nodes. Voltage variables are assigned at the remaining essential nodes, and Kirchhoff's current law is used to write one equation per voltage variable. The number of equations is n-1, where n is the number of essential nodes.
The mesh-current method works only with planar circuits. Mesh currents are assigned to each mesh, and Kirchhoff's voltage law is used to write one equation per mesh. The number of equations is b-(n-1), where b is the number of branches in which the current is unknown, and n is the number of nodes. The mesh currents are used to find the branch currents.
Several new circuit simplification techniques were introduced in this chapter:
Source transformations allow us to exchange a boltage source(vs) and a series resistor(R) for a current source(is) and a parallel resistor(R) and vice versa. The combinations must be equivalent in terms of their terminal voltage and current. Terminal equivalence holds provided that is=vs/R
Thevenin equivalents and Norton equivalents allow us to simplify acircuit comprised of sources and resistors into an equivalent circuit consisting of a voltage source and a series resistor(Thevenin) or a current source and a parallel resistor(Norton). The simplified circuit and the original circuit must be equivalent in terms of their terminal voltage and current. Thus keep in mind that (1) the Thevenin voltage (Vth) is the open-circuit voltage across the terminals of the original circuit,(2) the Thevenin resistance (Rth) is the ratio of the Thevenin voltage to the short-circuit current across the terminals of the original circuit; and (3) the Norton equivalent is obtained by performing a source transformation on a Thevenin equivalent.
Maximum power transfer is technique for calculation the maximum value of p that can be delivered to a load, Tl. Maximumpower transfer occurs when Rl=Rth, the Thevenin resistance as seen from the resistor Tl. The equation for the maximum power transferred is p=Vth^2/4Rl
In a circuit with multiple independent sources, superposition allows us to activate one source at a time and sum the resulting voltages and currents to determine the voltage and currents that exist when all independent sources are active. Dependent sources are never deactivated when applying superposition.
Table 1.1 summarizes the base SI units; Table 1.2 presents some useful derived Si units.
Circuit analysis is based on the variables of voltage and current.
Voltage is the energy per unit charge created by charge separation and has the SI unit of volt(v=dq/dq).
Current is the rate of charge flow and has the SI unit of ampere(i=dq/dt).
The ideal vasic circuit element is a two-terminal component that cannot be subdivided; it can be described mathematically in terms of its terminal voltage and current.
The passive sign convention uses a positive sign in the expression thatrelates the voltage and current at the terminals of an element when the reference direction for the current through the element is in the direction of the reference voltage drop across the element.
Power is energy per unit of time and is equal to the product of the terminal voltage and current; it has the SI unit of watt(p=dq/dt=vi).
The algebraic sign of power is interpreted as follows:
If P>0, power is being delivered to the circuit or circuit component.
If P<0, power is being extracted from the circuit or circuit component.
The circuit elements introduced in this chapter are voltage sources, current sources, and resistors:
An ideal voltage source maintains a prescribed voltage regardless of the current in the divice. An ideal current source maintains a presscribed current regardless of the voltage across the divice. Voltage and current sources are either voltage in the circuit; or dependent, that is, determined by some other current or voltage in the circuit.
A resistor constrains its voltage and current to be proportional to each other. The value of the proportional constant relating voltage and current in a resistor is called its resistance and is measured in ohms.
Ohm's law establishes the proportionality of voltage and current in a resistor. Specifically.
v=iR
if the current flow in the resistor is in the direction of the voltage drop across it, or v=-iR
if the current flow in the resistor is in the direction of the voltage rise across it.
Vy com bining the equation for power, p=vi, with Ohm's law, we can determine the power absorbed by a resistor;
p=i^2R=v^2/R
Circuits are described by nodes and closed paths. A node is a point where two or more circuit elements join. When just two closed path is a loop traced through connecting elements, startnodes only once each.
The voltage and currents of interconnected circuit elements obey Kirchhoff's laws:
Kirchhoff's current law states that the algebraic sum of all the currents at any node in a circuit equals zero.
Kirchhoff's valtage law states that the algebraic sum of all the voltages around any closed path in a circuit equals zero
A circuit is solved when the voltage across and the current in every element have been determined. By combining an understanding of independent and dependent sources, Ohm's law, and Kirchhoff's laws, we can solve many simple circuits.
Series resistors can be combined to obtain a single equivalent resistance according to the equation
Parallel resistors can be combined to obtain a single equivalent resistance according to the equation
When just two resistors are in parallel, the equation for equivalent resistance can be simplified to give
When voltage is divided across series resistors, as shown in the figure, the voltage across each resistor can be found according to the equations
When current is divided across parallel resistors, as shown in the figure, the current through each resistor can be found according to the equations
A voltmeter measures voltage and must be placed in parallel with the voltage being measured, An ideal voltmeter has infinite internal resistance and thus does not alter the voltage being measured.
An ammeter measures current and must be placed in series with the current being measured. An ideal ammeter has zero internal resistance and thus does not alter the current being measured.
Digital meters and analog meters have internal resistance, which influences the value of the circuit variable being measured.meters based on the d'Arsonval meter movement deliberately include internal resistance as a way to limit the current in the movement's coil.
The Wheatstone bridge circuit is used to make precise measurements of a resistor's value using four resistors,a dc voltage source, and a galvanometer.A Wheatstone bridge is balanced when the resistors obey Eq.(3.29), resulting in a galvanometer reading of 0A.
A circuit with three resistors connected in a Δ configuration(or a π configuration) can be transformed into an equivalent circuit in which the three resistors are Y connected(of T connected).The Δ-to-Y transformation is given by Eqs.(3.40)-(3.42); the Y-to-Δ transformation is given by Eqs.(3.43)-(3.45).
For the topics in this chapter,mastery of some basic terms, and the concepts they represent, is necessary. Those terms are node, planar circuit. Table 4.1 provides defiritions and examples of these terms.
Two new circuit analysis techniques were introduced in this chapter:
The node-coltage method works with both planar and nonplanar circuits. Areference node is chosen from among the essential nodes. Voltage variables are assigned at the remaining essential nodes, and Kirchhoff's current law is used to write one equation per voltage variable. The number of equations is n-1, where n is the number of essential nodes.
The mesh-current method works only with planar circuits. Mesh currents are assigned to each mesh, and Kirchhoff's voltage law is used to write one equation per mesh. The number of equations is b-(n-1), where b is the number of branches in which the current is unknown, and n is the number of nodes. The mesh currents are used to find the branch currents.
Several new circuit simplification techniques were introduced in this chapter:
Source transformations allow us to exchange a boltage source(vs) and a series resistor(R) for a current source(is) and a parallel resistor(R) and vice versa. The combinations must be equivalent in terms of their terminal voltage and current. Terminal equivalence holds provided that is=vs/R
Thevenin equivalents and Norton equivalents allow us to simplify acircuit comprised of sources and resistors into an equivalent circuit consisting of a voltage source and a series resistor(Thevenin) or a current source and a parallel resistor(Norton). The simplified circuit and the original circuit must be equivalent in terms of their terminal voltage and current. Thus keep in mind that (1) the Thevenin voltage (Vth) is the open-circuit voltage across the terminals of the original circuit,(2) the Thevenin resistance (Rth) is the ratio of the Thevenin voltage to the short-circuit current across the terminals of the original circuit; and (3) the Norton equivalent is obtained by performing a source transformation on a Thevenin equivalent.
Maximum power transfer is technique for calculation the maximum value of p that can be delivered to a load, Tl. Maximumpower transfer occurs when Rl=Rth, the Thevenin resistance as seen from the resistor Tl. The equation for the maximum power transferred is p=Vth^2/4Rl
In a circuit with multiple independent sources, superposition allows us to activate one source at a time and sum the resulting voltages and currents to determine the voltage and currents that exist when all independent sources are active. Dependent sources are never deactivated when applying superposition.
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