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slide 1 In the circuit represented by these graphs, the current ____ the voltage A. leads B. lags C. is less than D. is in phase with RLC Circuits
slide 1
In the circuit represented by these graphs, the current ____ the voltage
A. leadsB. lags C. is less thanD. is in phase with
RLC Circuits
slide 2
In the circuit represented by these graphs, the current ____ the voltage
A. leadsB. lags C. is less thanD. is in phase with
RLC Circuits
slide 3
RLC Circuit
slide 4
RLC Circuits
We need to add the three voltages:
slide 5
RLC Circuits
This will give the source voltage:
There is a phase angle between current and source voltage.
slide 6
RLC Circuits
Note:
slide 7
RLC Circuits
Adding sinusoids of different phase and amplitude, but all at the same frequency yields another sinusoid:
You can prove this with trigonometric identities or with phasors.
slide 8
Phasors
An oscillating function is like the x-component of a rotating vector.
slide 9
Phasors
slide 10
Phasors
Our textbook follows the vertical component of the phasor.
We will consider the horizontal component. This is the more common convention.
Vectors are related to complex numbers by “Euler’s Formula”:
Following the x-component is like taking the Real part of the complex function:
slide 11
This is a current phasor. The magnitude of the instantaneous value of the current is
A. Increasing.
B. Decreasing.
C. Constant.
D. Can’t tell without knowing which way it is rotating.
Phasors
slide 12
This is a current phasor. The magnitude of the instantaneous value of the current is
A. Increasing.
B. Decreasing.
C. Constant.
D. Can’t tell without knowing which way it is rotating.
Phasors
slide 13
current and voltage are in phase, both oscillating as
Resistors:
Phasors
slide 14
Phasors
slide 15
current peaks one-quarter period before the voltage peaks
Phasors
Capacitors:
slide 16
Phasors
slide 17
● current peaks one-quarter period after the voltage peaks
Phasors
Inductors:
slide 18
Phasors
slide 19
In the circuit represented by these phasors, the current ____ the voltage
A. leadsB. lagsC. is perpendicular toD. is out of phase with
Phasors
slide 20
In the circuit represented by these phasors, the current ____ the voltage
A. leadsB. lags C. is perpendicular toD. is out of phase with
Phasors
slide 21
Phasors
slide 22
Phasors
slide 23
Phasors
slide 24
Adding sinusoids of different phase and amplitude, but all at the same frequency yields another sinusoid.
Phasors
slide 25
Adding sinusoids of different phase and amplitude, but all at the same frequency yields another sinusoid.
Phasors
slide 26
Does VR + VC = 0?
A. YesB. No.C. Can’t tell without knowing ω.
Instantaneous voltages add.Peak voltages don’t because the voltages are not in phase.
slide 27
Current amplitude is related to voltage amplitude:
Impedance
called the capacitive reactanceunits: ohms (Ω)
Capacitors:
slide 28
Current amplitude is related to voltage amplitude:
Impedance
called the inductive reactanceunits: ohms (Ω)
Inductors:
slide 29
Current amplitude is related to voltage amplitude:
Impedance
Resistors:
slide 30
Phase Angle in a Series RLC Circuit
slide 31
Reactance and resistance are both forms of impedance (Z) to AC current flow.
Impedance
impedance, units: ohms (Ω)
slide 32
Reactance and resistance are both forms of impedance (Z) to AC current flow.
Impedance
lower impedance at high freq.
higher impedance at high freq.
slide 33
Impedance
slide 34
For a DC circuit, most of the voltage lies across the greatest resistance.
Impedance
slide 35
For an AC circuit, most of the voltage lies across the greatest impedance.
Impedance
slide 36
RC Filter Circuits
a low-pass filter.
slide 37
RC Filter Circuits
a high-pass filter.
slide 38
Impedance
largeinductance
small inductance
low reactance
slide 39
An AC circuit has least impedance at the frequency where :
called the resonant frequency
Resonance
slide 40
a series RLC circuit driven below the resonance frequency: ω < ω0
XL < XC, and ϕ is negative.
Resonance
slide 41
a series RLC circuit driven at the resonance frequency: ω = ω0
XL = XC, and ϕ = 0
Resonance
slide 42
a series RLC circuit driven above the resonance frequency: ω > ω0
XL > XC, and ϕ is positive.
Resonance
slide 43
Resonance
little current at very low or very high frequencies.
I is maximum when XL = XC, which occurs at the resonance frequency:
slide 44
If the value of R is increased, the resonance frequency of this circuit
A. Increases.B. Decreases. C. Stays the same.
slide 45
If the value of R is increased, the resonance frequency of this circuit
A. Increases.B. Decreases. C. Stays the same.
The resonance frequency depends on C and L but not on R.
slide 46
The resonance frequency of this circuit is 1000 Hz. To change the resonance frequency to 2000 Hz, replace the capacitor with one having capacitance
A. C/4B. C/2 C. 2CD. 4CE. It’s impossible to change the resonance frequency
by changing only the capacitor.
slide 47
The graphs show the instantaneous power loss in a resistor R carrying a current iR:
Power
The average power PR is the total energy dissipated per second:
slide 48
Power
instantaneous power loss in a resistor R carrying a current iR:
slide 49
We can define the root-mean-square current and voltage as
Power
The resistor’s average power loss in terms of the rms quantities is
The power rating on a lightbulb is its average power at Vrms = 120 V.
I rms IR2
Vrms VR2
slide 50
Power
slide 51
Energy flows into and out of a capacitor as it is charged and discharged.
The energy is not dissipated, as it would be by a resistor.
The energy is stored as potential energy in the capacitor’s electric field.
Power
slide 52
The instantaneous power flowing into a capacitor is
Power
slide 53
Energy is supplied by the emf and dissipated by the resistor. The average power supplied by the emf is:
Power
The term cos ϕ, called the power factor, arises because the current and the emf are not in phase.
maximum work per second when the power factor is as close to 1 as possible.
