RLC + Power

Question 1

How do you calculate True Power?

What is True Power?

Answer 1

Irms^2 * R

Power dissipated by the resistor

Question 2

How do you calculate reactive Power?

What is reactive Power?

Answer 2

Power stored and released by the capacitor or inductor

Irms^2 * XL or Irms^2*Xc

Question 3

How do you calculate apparent Power?

What is apparent Power?

Answer 3

Phasor sum of Reactive and True power

Irms^2 * Z
Vrms * Irms

Question 4

How do you calculate Reactive Power and True power form apparent power?

Answer 4

Question 5

What is the Unit of True power

Answer 5

Watts

Question 6

What is the unit of Apparent Power

Answer 6

VA (Volt ampare)

Question 7

What is the unit of Reactive power

Answer 7

VAR (volt ampere reactive)

Question 8

Derive the Transient response Differential Equation for an RLC circuit

Explain the solution

Answer 8

Solution has two parts the transient and steady state response.

i = i(transient) + i(steady state)

Question 9

Explain the Characteristics of an Underdamped responce

Answer 9

LCR circuit experiences decaying oscillations (ringing) at the natural frequency of the system

Question 10

Explain the Characteristics of an overdamped response

Answer 10

response has a peak and a decaying exponential

Question 11

Explain the Characteristics of a critically damped response

Answer 11

responce has a peak and exponential that decays to zero in the shortest possible time

Question 12

Explain how the solution to the LCR transient response differential equation can tell you if a system is over, under or critically damped.

Answer 12

Question 13

why can we ignore the steady state response in an RLC circuit?

Answer 13

capacitor prevents current flowing in this condition.

Question 14

explain how to calculate the impedance of an RLC circuit that is connected to a sinusoidal voltage and the phase angle

Answer 14

Question 15

calculate the peak current and phase angle of the following circuit,

Answer 15

Question 16

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

Answer 16

Due to the Capacitor and inductor connected in series there will be a frequency where the current increases to a peak value.

Question 17

Explain the conditions needed for a LCR circuit to be at resonance

What frequency does this occur at

Answer 17

Impedance of Inductor = Impedance of Capacitor

therefore
V(inductor) = V(Capacitor)
V(resistor) =V(supply)

Question 18

How do you derive the formula that calculates the frequency for resonance of a series RLC Circuit?

Answer 18

Question 19

Explain why Apparent Power is equal to true Power at resonance of a series RLC Circuit?

Answer 19

Reactive Components cancel out at resonance
Phasor sum of 0 and True power = True power

Question 20

Draw the Phase Diagram of an LCR Circuit

Answer 20

Question 21

What is Q Factor

Answer 21

Ratio of Reactive Power in Capacitor or inductor

and average power in the Resistor

Question 22

What does a High Q Factor imply

What does a Low Q imply

Answer 22

Sharp Resonance Peak with Narrow Width

Broad Resonance Peak with wide Width

Question 23

What is Q Factor in terms of energy

Answer 23

Ratio of Energy stored in the Circuit

and the energy dissipated per cycle

Question 24

How does Q Factor Impact the damping of the transient state

Answer 24

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

Question 25

Derive an Equation for Q Factor in terms of Resistance Inductance and Capacitance

Answer 25

Question 26

Explain why care must be taken with RLC circuits at resonance

Answer 26

Voltage across inductor and capacitor is the same Both can go much higher then the voltage supply at resonance

Question 27

What is another formula for Q Factor in terms of bandwidth

Answer 27

Question 28

What is the Bandwidth in a LCR circuit How do you calculate the bandwidth.

Answer 28

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)

Question 29

Derive how to calculate Bandwith from an RLC Circuit.

Answer 29

Question 30

Draw a Bandpass Filter using a Capacitor and inductor

Answer 30

Question 31

Draw a bandstop filter using a capacitor and inductor What does a band stop do?

Answer 31

Sharp decrease of current near a specific frequency

Question 32

How do you calculate the Voltage across a Band pass filter made from Capacitors and Inductors

Answer 32

Question 33

Draw a Tank Circuit Explain the what happens

Answer 33

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

Question 34

What happens to a tank circuit at resonance

Answer 34

it draws no current for the power supply effectively becoming a brick wall. where no current can pass through Infinite resistance