Worksheet 18-Resonant Circuit Operation

Question 1

What is resonance in an RCL circuit?

Answer 1

Resonance is when the inductive reactance and the capacitive reactance in a circuit are equal.

Question 2

What variable allows an RCL to operate at resonance?

Answer 2

The input frequency is what allows a circuit to operate at resonance.

Question 3

What two components in an RCL circuit determine the resonance frequency?

Answer 3

The value of the capacitor and the value of the inductor determine what frequency resonance occurs at.

Question 4

What is the relationship between current and impedance in a series RCL circuit operating at resonance?

Answer 4

In a series RCL circuit, current is at minimum and impedance is at maximum.

Question 5

Refer to the diagram to answer the question:
Identify which is the upper Hpp

Answer 5

Position C

Question 6

Refer to the diagram to answer the question:
What is used to determine the bandwidth in this diagram?

Answer 6

Distance between A and C

Question 7

Refer to the diagram to answer the question:
What is item D measuring?

Answer 7

D is point where the current value is 70.7% of its maximum resonant value, which is defined as (0.707 x I)²R. This level corresponds to the lower frequency half power level, called the “lower cut-off frequency” and the upper frequency cut-off. The distance between these two points is called Bandwidth and is the range of frequencies over which at least half the maximum power and current is provided.

Question 8

Given an f1 of 122MHz and f2 of 126MHz, what is the bandwidth?

Answer 8

Bandwidth is 4MHz

Question 9

Determine the resonant frequency of an RCL circuit given:

Capacitor = 6μF

Inductor = 50mH

Resistor = 20Ω

Answer 9

• f_R = 1 /(2∏√LC)*
• f_R = 1 /(2∏√0.05 x 0.000006)*
• f_R = 1 /(2∏ x 0.000547723)*
• f*_R = 1 /0.003441442
• f*_R = 290.57Hz

Question 10

Determine the resonant frequency of an RCL circuit given:

Capacitor = 15μF

Inductor = 10H

Resistor = 100kΩ

Answer 10

• f_R = 1 /(2∏√LC)*
• f_R = 1 /(2∏√10 x 0.000015)*
• f_R = 1 /(2∏ x 0.012247448)*
• f*_R = 1 /0.0769139779
• f*_R = 13kHz

Question 11

What is Q as it refers to in an AC circuit?

Answer 11

Q is “Quality Factor.” Q in a circuit refers to the quality of the operation of a circuit at resonance. The bandwidth of a circuit determines the Q.

Question 12

How is Q classified and identified?

Answer 12

Q is classified as either High Q with a tall and narrow bandwidth or Low W, with a low and wide bandwidth.