RLC + Power Flashcards
How do you calculate True Power?
What is True Power?
Irms^2 * R
Power dissipated by the resistor
How do you calculate reactive Power?
What is reactive Power?
Power stored and released by the capacitor or inductor
Irms^2 * XL or Irms^2*Xc
How do you calculate apparent Power?
What is apparent Power?
Phasor sum of Reactive and True power
Irms^2 * Z
Vrms * Irms
How do you calculate Reactive Power and True power form apparent power?
What is the Unit of True power
Watts
What is the unit of Apparent Power
VA (Volt ampare)
What is the unit of Reactive power
VAR (volt ampere reactive)
Derive the Transient response Differential Equation for an RLC circuit
Explain the solution
Solution has two parts the transient and steady state response.
i = i(transient) + i(steady state)
Explain the Characteristics of an Underdamped responce
LCR circuit experiences decaying oscillations (ringing) at the natural frequency of the system
Explain the Characteristics of an overdamped response
response has a peak and a decaying exponential
Explain the Characteristics of a critically damped response
responce has a peak and exponential that decays to zero in the shortest possible time
Explain how the solution to the LCR transient response differential equation can tell you if a system is over, under or critically damped.
why can we ignore the steady state response in an RLC circuit?
capacitor prevents current flowing in this condition.
explain how to calculate the impedance of an RLC circuit that is connected to a sinusoidal voltage and the phase angle
calculate the peak current and phase angle of the following circuit,
Explain what is meant by series resonance in a LCR Circuit
When does this Occur
What is the impedance at resonance
what is the frequency which resonance happens
Due to the Capacitor and inductor connected in series there will be a frequency where the current increases to a peak value.
Explain the conditions needed for a LCR circuit to be at resonance
What frequency does this occur at
Impedance of Inductor = Impedance of Capacitor
therefore
V(inductor) = V(Capacitor)
V(resistor) =V(supply)
How do you derive the formula that calculates the frequency for resonance of a series RLC Circuit?
Explain why Apparent Power is equal to true Power at resonance of a series RLC Circuit?
Reactive Components cancel out at resonance
Phasor sum of 0 and True power = True power
Draw the Phase Diagram of an LCR Circuit
What is Q Factor
Ratio of Reactive Power in Capacitor or inductor
and average power in the Resistor
What does a High Q Factor imply
What does a Low Q imply
Sharp Resonance Peak with Narrow Width
Broad Resonance Peak with wide Width
What is Q Factor in terms of energy
Ratio of Energy stored in the Circuit
and the energy dissipated per cycle
How does Q Factor Impact the damping of the transient state
High Q factor means the circuit is less damped
Sustains oscillations for a longer period of time
Low Q factor means the circuit is more damped
Oscillations Decay More Quickly
Derive an Equation for Q Factor in terms of Resistance Inductance and Capacitance
Explain why care must be taken with RLC circuits at resonance
Voltage across inductor and capacitor is the same
Both can go much higher then the voltage supply at resonance
What is another formula for Q Factor in terms of bandwidth
What is the Bandwidth in a LCR circuit
How do you calculate the bandwidth.
the difference between the two values of apparent power that equal 1/2 of the power of the resonant peak.
Reduce the current by a factor of root(2), or reduce impedance by a factor of root(2)
Derive how to calculate Bandwith from an RLC Circuit.
Draw a Bandpass Filter using a Capacitor and inductor
Draw a bandstop filter using a capacitor and inductor
What does a band stop do?
Sharp decrease of current near a specific frequency
How do you calculate the Voltage across a Band pass filter made from Capacitors and Inductors
Draw a Tank Circuit
Explain the what happens
Capacitor charges Up
Capacitor discharges
Inductor magnetic field strength increases, applied in the opposing direction to current flow
The inductor magnetic field applies to oppose the current dropping to zero, in turn charging the capacitor .
Capacitor discharges , but sending current in the opposite direction to as before.
Repeat Steps 3,4
This whole process then repeats
What happens to a tank circuit at resonance
it draws no current for the power supply
effectively becoming a brick wall. where no current can pass through
Infinite resistance
