MindMap Gallery Sinusoidal AC circuit 1
This is a mind map about sinusoidal AC circuit 1, including: the three elements of sinusoidal quantities, the representation method of sinusoidal quantities, sinusoidal AC circuits with a single parameter, series and parallel impedances, and resonance in the circuit.
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sinusoidal ac circuit
Three elements of sinusoidal quantities
initial phase Ψ
definition
The starting position of the sine quantity
phase difference
φ=ψ1-ψ2, if >0 it means 1 leads 2φ angle, <0 means 1 lags 2φ angle.
Note: ① It is meaningful when compared with the same frequency ② The phase difference has nothing to do with the selection of timing starting point
Amplitude Im
definition
The size of the sine quantity
three kinds
Instantaneous value (i,u) lowercase
Amplitude (Im, Um) must contain m
Valid value U=Um/√2
①The current and voltmeter measurement data are all valid values
②The current and voltage marked on the nameplate of the AC equipment are valid values.
Angular frequency ω
definition
How fast the sinusoidal quantity changes
cycle
The time it takes for a sinusoidal quantity to change for one week. f=1/T ω=2π/T=2πf
How to express sinusoidal quantity
Waveform graph
instantaneous value expression
u=Umsin(ωtφ)
phasor representation
3 representations of plural numbers
①Algebraic formula A=a jb=r(cosψ jsinψ)
②Exponential formula A=re^(jψ)
③Polar coordinate formula A=r∠ψ
Single parameter sinusoidal AC circuit
Series AC circuits of resistive, inductive and capacitive elements (RLC series circuits)
The relationship between voltage and current
①The current flowing through each component is the same
②The instantaneous voltage value of each part satisfies Kirchhoff’s law
Represent voltage or current using phasor method and phasor diagram
①phasor method
U=UR UL UC (phasor means adding points) =I[R j(XL-XC)] (I is also expressed as a phasor)
②Phaseor diagram
power
Impedance, voltage, power triangle
Impedance in series and parallel
Calculation method
①Phaseor diagram method
First select the reference phasor (sine quantity with initial phase set to zero)
②Sequence phasor formula
Notice
The operation of series and parallel impedance is a complex operation rather than an algebraic operation
Resonance in a circuit
definition
In a circuit containing an inductor and a capacitor, there is a phase difference between the voltage and current. If the frequency of the adjusted power supply or the circuit parameters are u and i in the same direction, the circuit is fully compensated for the reactive power, and the power factor of the circuit cosφ=1, the circuit is said to be in a resonant state.
series resonance
condition
cosφ=1, the condition for u and i to be in phase is: XL=XC
Features
①The current reaches the maximum value
②The voltage on L and C may exceed the total voltage
resonance curve
Resonance curve: the relationship between current and frequency.
parallel resonance
Improvement of power factor
definition
Average power P=UIcosφ. cosφ is the power factor
Dangers of low power factor
①The capacity of power generation equipment cannot be fully utilized
②Increase the power loss of lines and motor windings
How to improve power factor
Principle: Reduce the potential difference between voltage and line current without changing the load operating conditions.
Method: Add capacitive components
Ways to increase the power of inductive circuits: parallel capacitors