15 questions

(5 points) Find the reactance of a 100mH inductor at 1kHz. Show your work for partial credit.

(5 points) Find the reactance of a 1uF capacitor at 1MHz. Show your work for partial credit.

For problems 3 through 6, consider the following series resonant circuit (assume perfect components):

(10 points) Find the total impedance of the circuit at 1kHz. Show your work for partial credit.

For problems 4-7, assume that the signal generator frequency is changed to the natural resonant frequency of the circuit (I.E. it is no longer at 1kHz).

(10 points) Find the natural resonant frequency of the circuit. Show your work for partial credit.

(5 points) Find the impedance of the inductor in the circuit at resonance. Use your result for #4. Show your work for partial credit.

(5 points) Find the Q of the above circuit, using your result for #5 and any other relevant information from the schematic. Show your work for partial credit.

(5 points) Finally, find the bandwidth of the above circuit, using your results above. Show your work for partial credit.

(5 points) Describe the behavior of a real inductor (such as the 100mH ones we used in lab) at steady-state DC. Assume that this is a real inductor, not a theoretically perfect one.

Hint: A perfect inductor only has reactance…

(5 points) Describe the behavior of a real capacitor at steady-state DC. (This is similar to, but not identical to, the behavior of a perfect capacitor.)

(5 points) In the following circuit (at resonance, using perfect components), zero voltage is present across the LC pair, even though the signal generator is on and working. Why is this? (Hint: the meter is working correctly and set up correctly. There is a theoretical reason why you would expect zero voltage here, at resonance.)

(5 points) Simplify the following expression, to produce a single complex number of the form a + bi. Show your work for partial credit.

(20+10i)/(1+2i)

(11 points) You have an oscilloscope displaying the following waveform (Channel 1):

Describe how to do the following, by marking the relevant controls with the letter of the operation (A, B, C etc) and an arrow showing which way to turn the control:

Reduce the vertical size of the waveform

Move the reduced waveform to the top half of the screen

Change the horizontal scale to see more cycles on the screen

True or false: (3 points each)

In an inductor, current leads voltage. T F

In a capacitor, current leads voltage. T F

Capacitors are closer to “perfect” than inductors. T F

A series resonant circuit has maximum impedance T F at resonance.

A parallel resonant circuit has maximum impedance T F at resonance.

AC signals always have an average voltage of zero, T F since they go both positive and negative.

DC current can pass through a series resonant circuit. T F

DC current can pass through a parallel resonant circuit. T F

Extra credit (up to 10 points are possible, for a complete, correct design):

(This is somewhat challenging, so you should do the above problems first…)

You have been asked to design a bandpass filter to receive the radio station WWV, which broadcasts at a frequency of 10MHz. Design a resonant circuit at 10MHz using whatever components you want (capacitors from 0.1pF to 470uF are available, as are inductors from 0.1uH to 100mH and resistors from 1Ω to 1MΩ.)

Assume that all available components are textbook-perfect.

Your circuit should have the following characteristics:

A series-resonant design;

A resonant frequency of exactly 10MHz;

A bandwidth of exactly 20kHz.

Hint: Find the Q of the circuit that you will need to produce the desired bandwidth, and go from there.